Question

Consider the system of equations:
y
=
x
−
4
2
x
+
y
=
5
Which of these ordered pairs
(
x
,
y
)
are solutions to the system? Select all that apply by substituting each pair into both equations.
Select one answer
A
(
1
,
−
3
)

B
(
2
,
−
2
)

C
(
3
,
−
1
)

D
(
4
,
0
)

E
(
5
,
1
)

Answer 1

Only C, (3, −1).

Check each pair in both equations y = x − 4 and 2x + y = 5:

A (1, −3): y = 1 − 4 = −3 ✓, but 2(1) + (−3) = −1 ≠ 5 ✗
B (2, −2): y = 2 − 4 = −2 ✓, but 2(2) + (−2) = 2 ≠ 5 ✗
C (3, −1): y = 3 − 4 = −1 ✓, and 2(3) + (−1) = 5 ✓
D (4, 0): y = 4 − 4 = 0 ✓, but 2(4) + 0 = 8 ≠ 5 ✗
E (5, 1): y = 5 − 4 = 1 ✓, but 2(5) + 1 = 11 ≠ 5 ✗

Thus only (3, −1) satisfies both equations.