Math Pacing

Elimination Using Addition and Subtraction

1. The sum of two numbers is 31. The greater number is 5 more than the lesser number. What are the two numbers?

2. Complementary angles have a sum of 90°. Angles A and B are complementary and the measure of angle A is 14 ° less than the measure of angle B. Find the measures of angles A and B.

3. What value of c in the system of equations 5x + y = – 1 and – 2y = 10x + c will produce a system of equations with infinitely many solutions?

Let x = the greater numberLet y = the lesser number 5

31

yx

yx 315 yy262 y

13y

18x

Let x = the measure of ALet y = the measure of B 14

90

yx

yx 9014 yy1042 y

52y

38x

15 yx 15 xy 2102 xy 2c



Sometimes adding two equations together will eliminate one variable.

Using this step to solve a system of equations is called elimination.

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.

Elimination Using Addition

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

Simplify.

Add 60 to each side.


Simplify.

First equation

Replace y with –15.

Simplify.

Answer: The solution is (–24, –15).



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

Write and Solve a System of Equations

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.


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



Sometimes subtracting one equation from another will eliminate one variable.

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.


Simplify.

Elimination Using SubtractionUse elimination to solve the system of equations.

–

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.


Simplify.

Elimination Using Subtraction


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.


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


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