The sum of five times a number and twice a second number is 18, but the difference of three times the first number and seven times the second number is -22. Find the two numbers using the elimination method.
A. -2 and -4
B. -2 and 4
C. 2 and -4
D. 2 and 4

Question

The sum of five times a number and twice a second number is 18, but the difference of three times the first number and seven times the second number is -22. Find the two numbers using the elimination method.
	A.	-2 and -4
	B.	-2 and 4
	C.	2 and -4
	D.	2 and 4

texaschic101 · Answer

5x + 2y = 18 --->(3)
3x - 7y = -22 --->(-5)
------------------
15x + 6y = 54 (result of multiplying by 3)
-15x + 35y = 110 (result of multiplying by -5)
-----------------add
41y = 164
y = 4

now sub 4 in for y in either of the original equations
5x + 2y = 18
5x + 2(4) = 18
5x + 8 = 18
5x = 18 - 8
5x = 10
x = 2

check...
3x - 7y = -22
3(2) - 7(4) = -22
6 - 28 = -22
-22 = -22 (correct)

x = 2 and y = 4