### All College Algebra Resources

## Example Questions

### Example Question #11 : Equations With More Than One Variable

Solve for x and y in the following pair of equations

**Possible Answers:**

**Correct answer:**

There are two ways to solve for x and y in this pair of equations. First, you can add the two equations together and cancel out one of the variables. In this case, you can see that there is no need to multiply one of the equations by a positive or negative number, as y and -y already cancel each other out. The second way is to solve for one of the variables, then substitute that value into the other equation to solve for the other variable. In this case, I will show how to add both equations together to solve for x and y since the equations as they are cancel the y variable out.

after adding the two equations, the result is:

(note how the y variable eliminated itself)

Now just divide both sides by 7 to solve for x:

now just plug in the value of x into either equation to solve for y.

Let's pick the top equation:

now subtract 4 from each side to solve for y:

You can check your answers by plugging them into either equation, and since they are equations, both sides will be equal if your answers are correct.

### Example Question #21 : Solving Equations And Inequallities

Solve for x and y in the following pair of equations

**Possible Answers:**

**Correct answer:**

There are two ways to solve for x and y in this pair of equations. First, you can add the two equations together and cancel out one of the variables. In this case, you can see that there is no need to multiply one of the equations by a positive or negative number, as 2y and -2y already cancel each other out. The second way is to solve for one of the variables, then substitute that value into the other equation to solve for the other variable. In this case, I will show how to add both equations together to solve for x and y since the equations as they are cancel the y variable out.

You can see how adding the two equations cancel the y variable.

now just divide both sides by four to solve for x:

now just plug the value of x into either equation to solve for y.

Let's pick the top equation:

now subtract 1 from each side to isolate y:

now divide both sides by two to solve for y:

You can check your answers by plugging them into either equation, and since they are equations, both sides will be equal if the answers are correct.

### Example Question #31 : Solving Equations And Inequallities

Solve for x and y in the following pair of equations

**Possible Answers:**

**Correct answer:**

There are two ways to solve for x and y in a pair of equations. First, you can combine (add) the two equations together and eliminate one variable. In this case, that would require multiplying the top equation by -2 in order to eliminate the x variable, since 4x and -4x will cancel out, making it able to solve for y. The second method is to solve for one of the variables, then plug in its value into the other equation. Let's do this method for this problem. First, let's solve for x for the top equation:

First, isolate x by adding 2y to both sides:

Now divide both sides by -2 to solve for x:

So now, plug in this value into the other (bottom) equation to solve for y:

now add 24 to both sides to isolate y:

now just divide both sides by 7 to solve for y:

now plug in the value of y into either equation to solve for x:

Let's pick the top equation:

now add two to both sides to isolate x:

now divide both sides by -2 to solve for x:

You can check your answers by plugging them into either equation, and since it's an equation, both sides will be equal if your answers are correct.

### Example Question #32 : Solving Equations And Inequallities

Solve for x and y in the following pair of equations

**Possible Answers:**

**Correct answer:**

There are two ways to solve for x and y in a pair of equations. One way is to combine (add) the two equations together in order to eliminate one variable. In this case, to solve for y, you would have to multiply the top equation by -7 in order to negate the y variables. We will choose the second way, which is to solve for one of the variables then plug in that value into the other equation to solve for the other variable. If you look at both equations, solving for y on the top equation is easiest, so let's do that:

now just add 3x to both sides to solve for y:

now plug this value into the other (bottom) equation to solve for x:

now subtract 14 to both sides to isolate x:

now just divide both sides by 28 to solve for x:

now just plug in the value of x into either equation to solve for y.

Let's pick the top equation:

now just add 3 to both sides to solve for y:

You can check your answers by plugging them into either equation, and since they are equations, if both sides are equal, then you have the correct answers.

### Example Question #15 : Equations With More Than One Variable

Solve for x:

**Possible Answers:**

**Correct answer:**

Multiply the first equation by two.

Add both equations to cancel out the y-variable.

Divide by three on both sides.

The answer is:

### Example Question #451 : College Algebra

The town of Marysville is hosting its annual festival. For admission tickets, adults are charged $8, and children are charged $4. The town sold 2300 tickets and took in $13,688 in total ticket revenue. How many more children were admitted to the festival than adults?

**Possible Answers:**

72

56

100

88

64

**Correct answer:**

56

This question requires setting up two equations and then solving the system of two equations. One equation represents the total number of tickets sold, and the other equation represents the total revenue. Both equations will use the same two variables, and , for the number of children and adults who were admitted, respectively.

The first equation is the easier of the two. The sum of the number of children and the number of adults admitted to the fair will equal 2300.

The second equation will incorporate the price charged to children and adults

Children's tickets cost $4 and adults' tickets cost $8. The total amount of money raised was $13,688.

To solve the system of equations, you can eliminate one of the variables. One way to do this is via the elimination method. To eliminate

Now add the two equations together to eliminate a variable.

--------------------------------

Solve for .

Substitute into either of the original equations and solve for .

There were 1178 children and 1122 adults admitted to the festival. Finally, subtract the results.

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