# Algebra II : Elementary Operations

## Example Questions

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### Example Question #1 : Addition And Subtraction

Above is the menu at a coffee shop.

Jerry has a coupon that entitles him to a free butter croissant with the purchase of one large drink of any kind. The coupon says "limit one per coupon".

He decides to purchase a large espresso, a large cappucino, and two butter croissants. Disregarding tax, how much will he pay for them?

None of the other responses is correct.

Explanation:

The coupon will entitle him to one free croissant, so Jerry will pay for the large espresso, the large cappucino, and one butter croissant. The charge will be the sum of the three prices:

### Example Question #2 : Addition And Subtraction

Find the distance, , between point  and point .

Explanation:

Use the distance formula to solve this problem.

Plugging in our points A and B we get the following distance.

### Example Question #3 : Addition And Subtraction

Solve the equation by Substitution.

Explanation:

First, take the first equation and solve for x in terms of y.

From here, substitute the equation you found for x into the second equation and solve for y.

Now, substitute the y value found into the original equation and solve for x.

### Example Question #4 : Addition And Subtraction

Solve the equation by Elimination.

Explanation:

To solve this system of equations by elimination you first need to multiply the first equation by -2. This will allow the y terms to cancel when equation 1 and equation 2 are adding together.

Now solve for x.

Substitute the x value into the orginial equation and solve for y.

Subtract:

Explanation:

### Example Question #5 : Addition And Subtraction

Simplify, if possible:

Explanation:

There is only one like-term in the expression given, which is .

Add the like term.  The rest of the terms cannot be combined by adding or subtracting.

### Example Question #6 : Addition And Subtraction

Solve:

Explanation:

Simplify first by eliminating the parentheses. To do this you will need to distribute the coefficient term outside the parentheses to each term within the parentheses.

Next, combine like terms.

### Example Question #7 : Addition And Subtraction

Solve:

Explanation:

Since this number is  or greater, use the tens digit as a carry over.

Add the tens digits with the carry over.

Add the hundreds digit with the carry over.  The hundreds digit for the second number in the problem is zero.

Since there is no carry over and there is no thousands digit for the second number, the thousands digit of the answer is just .

Combine all the ones digits in chronological order from thousands to the ones digits.

### Example Question #8 : Addition And Subtraction

Solve:

Explanation:

In order to simplify this, we need to combine like-terms.  The coefficients of unlike terms cannot be combined.

Combine all the terms.

### Example Question #9 : Addition And Subtraction

Solve:

Explanation:

In order to solve the problem, first evaluate .

Borrow a one from the six in the tens digit in order to subtract the ones digit.

The six in the tens digit becomes a five.  Subtract the five with the tens digit of the second number.