Question

Solve the system of equations using the elimination method. Show your steps.13x+y=32y=−23x+10

Answer 1

The system is
1) 13x + y = 32
2) y = −23x + 10

Rewrite (2) in standard form: 23x + y = 10.

Now eliminate y by subtracting (2) from (1):
(13x + y) − (23x + y) = 32 − 10
13x + y − 23x − y = 22
−10x = 22
x = −11/5.

Substitute x into 13x + y = 32:
13(−11/5) + y = 32
−143/5 + y = 32
y = 32 + 143/5 = (160 + 143)/5 = 303/5.

Solution: (x, y) = (−11/5, 303/5). (You can check it satisfies y = −23x + 10.)