This question tests understanding that a system solution is the intersection point of graphs—the (x,y) satisfying both equations simultaneously shown where lines cross. Two linear equations graph as two lines; solution is where lines intersect (point on both lines): one intersection (different slopes, one solution), parallel (same slope different intercepts, no intersection/no solution), or same line (infinite points/infinite solutions). Both lines have slope 1 but different y-intercepts (2 and -3), so they are parallel and do not intersect. Verification confirms no common point satisfies both, classifying as no solutions. The correct choice is C, as A assumes intersection, B and D misclassify the type. Strategy: (1) graph both equations (or interpret given graph), (2) identify intersection (where lines cross, read coordinates), (3) verify algebraically (substitute x,y into both equations checking both true), (4) classify (intersecting once=one solution, parallel=no solution, same line=infinite). Connection: graph is visual (see solution location), algebra is exact (calculate precise coordinates), both show same information (intersection point = system solution). Mistakes: checking only one equation (must verify both), reading coordinates wrong (x,y order matters), claiming parallel lines meet.

This question tests understanding that a system solution is the intersection point of graphs—the (x,y) satisfying both equations simultaneously shown where lines cross. Two linear equations graph as two lines; solution is where lines intersect (point on both lines): one intersection (different slopes, one solution), parallel (same slope different intercepts, no intersection/no solution), or same line (infinite points/infinite solutions). Point (x,y) is solution if substituting into both equations gives true statements (x=2, y=5 in y=2x+1: 5=2(2)+1=5✓, and y=-x+7: 5=-(2)+7=5✓, both true so (2,5) solves system). To verify, set 2x+1 = -x+7, yielding 3x=6 so x=2, then y=5, confirming (2,5) as the intersection. The correct choice is B, as A reverses coordinates, C has wrong y, and D is unrelated. Strategy: (1) graph both equations (or interpret given graph), (2) identify intersection (where lines cross, read coordinates), (3) verify algebraically (substitute x,y into both equations checking both true), (4) classify (intersecting once=one solution, parallel=no solution, same line=infinite). Connection: graph is visual (see solution location), algebra is exact (calculate precise coordinates), both show same information (intersection point = system solution). Mistakes: checking only one equation (must verify both), reading coordinates wrong (x,y order matters), claiming parallel lines meet.

Tests understanding system solution is intersection point of graphs—the (x,y) satisfying both equations simultaneously shown where lines cross. Two linear equations graph as two lines; solution is where lines intersect (point on both lines): one intersection (different slopes, one solution), parallel (same slope different intercepts, no intersection/no solution), or same line (infinite points/infinite solutions). Point (x,y) is solution if substituting into both equations gives true statements (x=2, y=4 in y=x+2: $4=2+2=4$ ✓, and y=6-x: $4=6-2=4$ ✓, both true; but (1,5): $5=1+2=3$ ✗, though $5=6-1=5$ ✓, so only one true). The system intersects at (2,4), so points like (1,5) do not satisfy both equations. Any point not at the intersection, such as (1,5), is not a solution. A common error is checking only one equation, thinking a point on one line solves the system. Strategy: (1) graph both equations (or interpret given graph), (2) identify intersection (where lines cross, read coordinates), (3) verify algebraically (substitute x,y into both equations checking both true), (4) classify (intersecting once=one solution, parallel=no solution, same line=infinite). Connection: graph is visual (see solution location), algebra is exact (calculate precise coordinates), both show same information (intersection point = system solution). Mistakes: checking only one equation (must verify both), reading coordinates wrong (x,y order matters), claiming parallel lines meet.

This question tests understanding that a system solution is the intersection point of graphs—the (x,y) satisfying both equations simultaneously shown where lines cross. Two linear equations graph as two lines; solution is where lines intersect (point on both lines): one intersection (different slopes, one solution), parallel (same slope different intercepts, no intersection/no solution), or same line (infinite points/infinite solutions). Point (x,y) is solution if substituting into both equations gives true statements (x=4, y=3 in $y=\frac{1}{2}x+1$: $3=\frac{1}{2}(4)+1=3$ ✓, and $y=-x+7$: $3=-(4)+7=3$ ✓, both true so (4,3) solves system). Verification shows both equations hold true for (4,3), so it is the intersection point. The correct choice is A, as B checks only one, C incorrectly claims second false, and D says both false. Strategy: (1) graph both equations (or interpret given graph), (2) identify intersection (where lines cross, read coordinates), (3) verify algebraically (substitute x,y into both equations checking both true), (4) classify (intersecting once=one solution, parallel=no solution, same line=infinite). Connection: graph is visual (see solution location), algebra is exact (calculate precise coordinates), both show same information (intersection point = system solution). Mistakes: checking only one equation (must verify both), reading coordinates wrong (x,y order matters), claiming parallel lines meet.

Tests understanding system solution is intersection point of graphs—the (x,y) satisfying both equations simultaneously shown where lines cross. Two linear equations graph as two lines; solution is where lines intersect (point on both lines): one intersection (different slopes, one solution), parallel (same slope different intercepts, no intersection/no solution), or same line (infinite points/infinite solutions). Point (x,y) is solution if substituting into both equations gives true statements (x=2, y=5 in y=2x+1: 5=2(2)+1=5✓, and y=-x+7: 5=-(2)+7=5✓, both true so (2,5) solves system). The second equation 2y=4x+2 simplifies to y=2x+1, which is the same as the first, so they represent the same line with infinite intersection points. The system has infinitely many solutions, making choice C correct. A common error is not simplifying the second equation and thinking the slopes differ. Strategy: (1) graph both equations (or interpret given graph), (2) identify intersection (where lines cross, read coordinates), (3) verify algebraically (substitute x,y into both equations checking both true), (4) classify (intersecting once=one solution, parallel=no solution, same line=infinite). Connection: graph is visual (see solution location), algebra is exact (calculate precise coordinates), both show same information (intersection point = system solution). Mistakes: checking only one equation (must verify both), reading coordinates wrong (x,y order matters), claiming parallel lines meet.

Tests understanding system solution is intersection point of graphs—the (x,y) satisfying both equations simultaneously shown where lines cross. Two linear equations graph as two lines; solution is where lines intersect (point on both lines): one intersection (different slopes, one solution), parallel (same slope different intercepts, no intersection/no solution), or same line (infinite points/infinite solutions). Point (x,y) is solution if substituting into both equations gives true statements ($x=2$, $y=5$ in $y=2x+1$: $5=2(2)+1=5\checkmark$, and $y=-x+7$: $5=-(2)+7=5\checkmark$, both true so $(2,5)$ solves system). For this system, the lines $y=2x+1$ and $y=-x+7$ have different slopes ($2$ and $-1$), so they intersect at one point; solving $2x+1=-x+7$ gives $3x=6$, $x=2$, then $y=5$. The correct intersection point is $(2,5)$, which is choice A. A common error is reversing the coordinates to $(5,2)$, but the point must satisfy both equations in the order (x,y). Strategy: (1) graph both equations (or interpret given graph), (2) identify intersection (where lines cross, read coordinates), (3) verify algebraically (substitute x,y into both equations checking both true), (4) classify (intersecting once=one solution, parallel=no solution, same line=infinite). Connection: graph is visual (see solution location), algebra is exact (calculate precise coordinates), both show same information (intersection point = system solution). Mistakes: checking only one equation (must verify both), reading coordinates wrong (x,y order matters), claiming parallel lines meet.

Tests understanding system solution is intersection point of graphs—the $(x,y)$ satisfying both equations simultaneously shown where lines cross. Two linear equations graph as two lines; solution is where lines intersect (point on both lines): one intersection (different slopes, one solution), parallel (same slope different intercepts, no intersection/no solution), or same line (infinite points/infinite solutions). Point $(x,y)$ is solution if substituting into both equations gives true statements (for x=2, y=5 in $y=2x+1$: $5=2(2)+1=5$ ✓, and $y=-x+7$: $5=-(2)+7=5$ ✓, both true so $(2,5)$ solves system). For this system, substituting (3,4) into $y=x+1$ gives $4=3+1$ (true), and into $y=2x-2$ gives $4=6-2$ (true), so it lies on both lines. The point (3,4) is indeed the solution, making choice A correct. A common error is verifying only one equation and assuming it's the solution without checking the second. Strategy: (1) graph both equations (or interpret given graph), (2) identify intersection (where lines cross, read coordinates), (3) verify algebraically (substitute x,y into both equations checking both true), (4) classify (intersecting once=one solution, parallel=no solution, same line=infinite). Connection: graph is visual (see solution location), algebra is exact (calculate precise coordinates), both show same information (intersection point = system solution). Mistakes: checking only one equation (must verify both), reading coordinates wrong (x,y order matters), claiming parallel lines meet.

This question tests understanding that a system solution is the intersection point of graphs—the (x,y) satisfying both equations simultaneously shown where lines cross. Two linear equations graph as two lines; solution is where lines intersect (point on both lines): one intersection (different slopes, one solution), parallel (same slope different intercepts, no intersection/no solution), or same line (infinite points/infinite solutions). Both lines have slope 1 but different y-intercepts (2 and -3), so they are parallel and do not intersect. Verification confirms no common point satisfies both, classifying as no solutions. The correct choice is C, as A assumes intersection, B and D misclassify the type. Strategy: (1) graph both equations (or interpret given graph), (2) identify intersection (where lines cross, read coordinates), (3) verify algebraically (substitute x,y into both equations checking both true), (4) classify (intersecting once=one solution, parallel=no solution, same line=infinite). Connection: graph is visual (see solution location), algebra is exact (calculate precise coordinates), both show same information (intersection point = system solution). Mistakes: checking only one equation (must verify both), reading coordinates wrong (x,y order matters), claiming parallel lines meet.

This question tests understanding that a system solution is the intersection point of graphs—the (x,y) satisfying both equations simultaneously shown where lines cross. Two linear equations graph as two lines; solution is where lines intersect (point on both lines): one intersection (different slopes, one solution), parallel (same slope different intercepts, no intersection/no solution), or same line (infinite points/infinite solutions). Point (x,y) is solution if substituting into both equations gives true statements (x=3, y=5 in y=3x-4: 5=3(3)-4=5✓, and y=-x+8: 5=-(3)+8=5✓, both true so (3,5) solves system). To verify, set 3x-4 = -x+8, yielding 4x=12 so x=3, then y=5, confirming (3,5) as the intersection. The correct choice is A, as C reverses coordinates, and B and D are points not on both lines. Strategy: (1) graph both equations (or interpret given graph), (2) identify intersection (where lines cross, read coordinates), (3) verify algebraically (substitute x,y into both equations checking both true), (4) classify (intersecting once=one solution, parallel=no solution, same line=infinite). Connection: graph is visual (see solution location), algebra is exact (calculate precise coordinates), both show same information (intersection point = system solution). Mistakes: checking only one equation (must verify both), reading coordinates wrong (x,y order matters), claiming parallel lines meet.

This question tests understanding that a system solution is the intersection point of graphs—the (x,y) satisfying both equations simultaneously shown where lines cross. Two linear equations graph as two lines; solution is where lines intersect (point on both lines): one intersection (different slopes, one solution), parallel (same slope different intercepts, no intersection/no solution), or same line (infinite points/infinite solutions). Point (x,y) is solution if substituting into both equations gives true statements (x=2, y=5 in y=2x+1: 5=2(2)+1=5✓, and y=-x+7: 5=-(2)+7=5✓, both true so (2,5) solves system). To verify, set 2x+1 = -x+7, yielding 3x=6 so x=2, then y=5, confirming (2,5) as the intersection. The correct choice is B, as A reverses coordinates, C has wrong y, and D is unrelated. Strategy: (1) graph both equations (or interpret given graph), (2) identify intersection (where lines cross, read coordinates), (3) verify algebraically (substitute x,y into both equations checking both true), (4) classify (intersecting once=one solution, parallel=no solution, same line=infinite). Connection: graph is visual (see solution location), algebra is exact (calculate precise coordinates), both show same information (intersection point = system solution). Mistakes: checking only one equation (must verify both), reading coordinates wrong (x,y order matters), claiming parallel lines meet.