splash screen lesson 3 contents example 1elimination using addition example 2write and solve a...

Example 1 Elimination Using Addition

Example 2 Write and Solve a System of Equations

Example 3 Elimination Using Subtraction

Example 4 Elimination Using Subtraction

Use elimination to solve the system of equations.

Since the coefficients of the x terms, –3 and 3, are additive inverses, you can eliminate the x terms by adding the equations.

Write the equation in column form and add.

Notice that the x value is eliminated.

Divide each side by –2.

Simplify.

Now substitute –15 for y in either equation to find the value of x.

Simplify.

Add 60 to each side.

Divide each side by –3.

Simplify.

First equation

Replace y with –15.

Simplify.

Answer: The solution is (–24, –15).

Use elimination to solve the system of equations.

Answer: (2, 1)

Four times one number minus three times another number is 12. Two times the first number added to three times the second number is 6. Find the numbers.

Let x represent the first number and y represent the second number.

Four times one number minus

three times another number is 12.

Two times the first number added to

three times the second number is 6.

4x – 3y = 12

2x + 3y = 6

Use elimination to solve the system.

Notice that the y value is eliminated.

Divide each side by 6.

Simplify.

Write the equation in column form and add.

Now substitute 3 for x in either equation to find the value of y.

Answer: The numbers are 3 and 0.

First equation

Replace x with 3.

Simplify.

Subtract 12 from each side.

Simplify.

Divide each side by –3.

Simplify.

Four times one number added to another number is –10. Three times the first number minus the second number is –11. Find the numbers.

Answer: –3, 2

Use elimination to solve the system of equations.

Since the coefficients of the x terms, 4 and 4, are the same, you can eliminate the x terms by subtracting the equations.

Write the equation in column form and subtract.

Notice that the x value is eliminated.

Divide each side by 5.

Simplify.

Now substitute 2 for y in either equation to find the value of x.

Answer: The solution is (6, 2).

Second equation

Simplify.

Add 6 to each side.

Simplify.

Divide each side by 4.

Simplify.

Use elimination to solve the system of equations.

Answer: The solution is (2, –6).

Multiple-Choice Test Item

If and what is the value of y?A (3, –8) B 3 C –8 D (–8, 3)

Read the Test ItemYou are given a system of equations, and you are

asked to find the value of y.

Solve the Test ItemYou can eliminate the y terms by subtracting one equation from the other.

Write the equation in column form and subtract.

Notice that the y value is eliminated.

Divide each side by 14.

Simplify.

Now substitute 3 for x in either equation to solve for y.

Answer: C

Notice that B is the value of x and A is the solution of the system of equations. However, the question asks for the value of y.

First equation

Simplify.

Subtract 24 from each side.

Simplify.

Multiple-Choice Test Item

If and what is the value of x?A 4 B (4, –4) C (–4, 4) D –4

Answer: D