Question

What is the solution of the system of equations shown?
3
x
+
2
y
=
8

5
x
+
2
y
=
12

A.
(
−
2
,
7
)
B.
(
2
,
1
)
C.
(
4
3
,
2
)
D.
(
2
,
4
)

Answer 1

Subtract the first equation from the second: (5x+2y) − (3x+2y) = 12 − 8 ⇒ 2x = 4 ⇒ x = 2.
Plug into 3x + 2y = 8: 6 + 2y = 8 ⇒ 2y = 2 ⇒ y = 1.

Solution: (2, 1) — choice B.