Question

Solve the system of equations using elimination.
5
x
−
4
y
=
12
2
x
+
3
y
=
−
1
What is the solution
(
x
,
y
)
?
Select one answer
A
(
−
29
23
,
32
23
)

B
(
32
23
,
−
29
23
)

C
(
29
23
,
32
23
)

D
(
32
23
,
29
23
)

Answer 1

Multiply the first equation by 3 and the second by 4 to eliminate y:
15x − 12y = 36
8x + 12y = −4
Add: 23x = 32 → x = 32/23.
Substitute into 2x + 3y = −1:
2(32/23) + 3y = −1 → 64/23 + 3y = −1 → 3y = −87/23 → y = −29/23.

So (x, y) = (32/23, −29/23). Answer: B.