### All SAT Math Resources

## Example Questions

### Example Question #245 : Equations / Inequalities

Solve for .

**Possible Answers:**

**Correct answer:**

For the second equation, solve for in terms of .

Plug this value of y into the first equation.

### Example Question #1 : How To Evaluate Algebraic Expressions

A store sells 17 coffee mugs for $169. Some of the mugs are $12 each and some are $7 each. How many $7 coffee mugs were sold?

**Possible Answers:**

8

6

7

10

9

**Correct answer:**

7

The answer is 7.

Write two independent equations that represent the problem.

*x* + *y* = 17 and 12*x* + 7*y* = 169

If we solve the first equation for *x*, we get *x* = 17 – *y* and we can plug this into the second equation.

12(17 – *y*) + 7*y* = 169

204 – 12*y* + 7*y* =169

–5*y* = –35

*y* = 7

### Example Question #261 : Equations / Inequalities

What is the value of in the following system of equations? Round your answer to the hundredths place.

**Possible Answers:**

**Correct answer:**

You can solve this problem in a number of ways, but one way to solve it is by using substitution. You can begin to do that by solving for in the first equation:

Now, you can substitute in that value of into the second equation and solve for :

Let's consider this equation as adding a negative 3 rather than subtracting a 3 to make distributing easier:

Distribute the negative 3:

We can now combine like variables and solve for :

### Example Question #2 : Creating Equations With Whole Numbers

What is the solution of for the systems of equations?

**Possible Answers:**

**Correct answer:**

We add the two systems of equations:

For the Left Hand Side:

For the Right Hand Side:

So our resulting equation is:

Divide both sides by 10:

For the Left Hand Side:

For the Right Hand Side:

Our result is:

### Example Question #3 : Creating Equations With Whole Numbers

What is the solution of that satisfies both equations?

**Possible Answers:**

**Correct answer:**

Reduce the second system by dividing by 3.

Second Equation:

We this by 3.

Then we subtract the first equation from our new equation.

First Equation:

First Equation - Second Equation:

Left Hand Side:

Right Hand Side:

Our result is:

### Example Question #248 : Equations / Inequalities

What is the solution of for the two systems of equations?

**Possible Answers:**

**Correct answer:**

We first add both systems of equations.

Left Hand Side:

Right Hand Side:

Our resulting equation is:

We divide both sides by 3.

Left Hand Side:

Right Hand Side:

Our resulting equation is:

### Example Question #4 : Creating Equations With Whole Numbers

What is the solution of for the two systems?

**Possible Answers:**

**Correct answer:**

We first multiply the second equation by 4.

So our resulting equation is:

Then we subtract the first equation from the second new equation.

Left Hand Side:

Right Hand Side:

Resulting Equation:

We divide both sides by -15

Left Hand Side:

Right Hand Side:

Our result is:

### Example Question #51 : Systems Of Equations

The cost of buying 1 shirt and 2 pants is $110 and cost of buying 4 shirts and 3 pants is $200. Assume that all shirts have the same cost and all pants have the same cost. What is the cost of one shirt and one pair of pants in dollars?

**Possible Answers:**

**Correct answer:**

Let s equal the cost of the shirt and p equal to the cost of a pair of pants. The question can be set up as follows:

The top equation can be multiplied by 4 to give:

The bottom equation can be subtracted from the top equation to give:

Dividing by 5 gives the cost of a pair of pants:

This can be plugged into either one of the initial equations to solve for the cost of the shirt.

Subtracting both sides by 96 gives:

The question asks for the cost of a pair of pants and a shirt which is the sume of the costs.

### Example Question #268 : Algebra

Solve for the point of intersection of the following two lines:

**Possible Answers:**

**Correct answer:**

Solve for or first. Let's solve for . To do this, we must eliminate the variables. Multiply the first equation by the coefficient of the variable in the second equation.

Subtract the second equation from the first equation and solve for .

Resubstitute this value to either original equations. Let's substitute this value into .

Find the common denominator and solve for the unknown variable.

The correct answer is:

### Example Question #51 : Systems Of Equations

If and , what is the value of ?

**Possible Answers:**

Cannot be determined

**Correct answer:**

If then adding is equal to . If then or . This means that is equal to or .