### All Algebra 1 Resources

## Example Questions

### Example Question #1 : How To Find The Solution For A System Of Equations

A cube has a volume of . If its width is , its length is , and its height is , find .

**Possible Answers:**

**Correct answer:**

Since the object in question is a cube, each of its sides must be the same length. Therefore, to get a volume of , each side must be equal to the cube root of , which is cm.

We can then set each expression equal to .

The first expression can be solved by either or , but the other two expressions make it evident that the solution is .

### Example Question #1 : How To Find The Solution For A System Of Equations

Solve the system for and .

**Possible Answers:**

**Correct answer:**

The most simple method for solving systems of equations is to transform one of the equations so it allows for the canceling out of a variable. In this case, we can multiply by to get .

Then, we can add to this equation to yield , so .

We can plug that value into either of the original equations; for example, .

So, as well.

### Example Question #2 : How To Find The Solution For A System Of Equations

What is the solution to the following system of equations:

**Possible Answers:**

**Correct answer:**

By solving one equation for , and replacing in the other equation with that expression, you generate an equation of only 1 variable which can be readily solved.

### Example Question #1 : How To Find The Solution For A System Of Equations

Solve this system of equations for :

**Possible Answers:**

None of the other choices are correct.

**Correct answer:**

Multiply the bottom equation by 5, then add to the top equation:

### Example Question #2 : How To Find The Solution For A System Of Equations

Solve this system of equations for :

**Possible Answers:**

None of the other choices are correct.

**Correct answer:**

Multiply the top equation by :

Now add:

### Example Question #3 : How To Find The Solution For A System Of Equations

Solve this system of equations for :

**Possible Answers:**

None of the other choices are correct.

**Correct answer:**

Multiply the top equation by :

Now add:

### Example Question #4 : How To Find The Solution For A System Of Equations

Find the solution to the following system of equations.

**Possible Answers:**

**Correct answer:**

To solve this system of equations, use substitution. First, convert the second equation to isolate .

Then, substitute into the first equation for .

Combine terms and solve for .

Now that we know the value of , we can solve for using our previous substitution equation.

### Example Question #5 : How To Find The Solution For A System Of Equations

Find a solution for the following system of equations:

**Possible Answers:**

infinitely many solutions

no solution

**Correct answer:**

no solution

When we add the two equations, the and variables cancel leaving us with:

which means there is no solution for this system.

### Example Question #9 : How To Find The Solution For A System Of Equations

Solve for :

**Possible Answers:**

None of the other answers

**Correct answer:**

First, combine like terms to get . Then, subtract 12 and from both sides to separate the integers from the 's to get . Finally, divide both sides by 3 to get .

### Example Question #6 : How To Find The Solution For A System Of Equations

We have two linear functions:

Find the coordinate at which they intersect.

**Possible Answers:**

none of these

**Correct answer:**

We are given the following system of equations:

We are to find and . We can solve this through the substitution method. First, substitute the second equation into the first equation to get

Solve for by adding 4x to both sides

Add 5 to both sides

Divide by 7

So . Use this value to find using one of the equations from our given system of equations. I think I'll use the first equation (can also use the second equation).

So the two linear functions intersect at