Page 190 - Math Course 2 (Book 1)

Systems of Equations: Elimination

Write and Solve a System of Elimination Using Subtraction
Equations

Example Example

Four times one number minus three times another
number is 12. Two times the f rst number added Use elimination to solve the system of equations.
to three times the second number is 6. Find the 4x + 2y = 28
numbers. 4x – 3y = 18

Let x represent the f rst number and y represent Since the coef cients of the x terms, 4 and 4, are
the second number. the same, you can eliminate the x terms by
subtracting the equations.
Four three
times times 4x + 2y = 28 Write the equations in column
one another (–) 4x – 3y = 18 form and subtract.
number minus number is 12
5y = 10 The x variable is eliminated.
4x – 3y = 12
5y = 10 Divide each side by 5.
three 5 5
Two times y = 2 Simplify.
times the
the f rst added second
number to number is 6
Now substitute 2 for y in either equation to f nd the
2x + 3y = 6 value of x.
Use elimination to solve the system. 4x – 3y = 18 Second equation

4x – 3y = 12 Write the equations in column 4x – 3(2) = 18 y = 2
(+) 2x + 3y = 6 form and add.
4x – 6 = 18 Simplify.
6x = 18 The y variable is eliminated.
4x – 6 + 6 = 18 + 6 Add 6 to each side.
6x = 18 Divide each side by 6.
6 6 4x = 24 Simplify.
x = 3 Simplify. 4x 24
4 = 4 Divide each side by 4.
Now substitute 3 for x in either equation to f nd the
value of y. x = 6 Simplify.
4x – 3y = 12 First equation.
Answer The solution is (6, 2)
4(3) – 3y = 12 Replace x with 3.

12 – 3y = 12 Simplify.

12 – 3y – 12 = 12 – 12 Subtract 12 from each side.

–3y = 0 Simplify.
3y 0
–3 = –3 Divide each side by –3.
y = 0 Simplify.

Answer The numbers are 3 and 0.

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