Question

Consider the system of equations:
2
x
−
3
y
=
−
7
4
x
+
y
=
1

Is the ordered pair
(
1
2
,
8
3
)
a solution to this system?
Select one answer
A
Yes, because it satisfies the first equation.

B
No, because it does not satisfy both equations.

C
No, because it does not satisfy the first equation.

D
Yes, because it satisfies both equations.

Answer 1

B

Substitute x = 1/2, y = 8/3:
2x − 3y = 2(1/2) − 3(8/3) = 1 − 8 = −7 (first equation holds).
4x + y = 4(1/2) + 8/3 = 2 + 8/3 = 14/3 ≠ 1 (second equation fails).
So the pair is not a solution because it does not satisfy both equations.