Question

Find the solution of the linear system graphically and check your solution.

x
+
y
=
−
1
3
x
−
y
=
5


__________________________________________________



(
−
1
,

1
)


image.png




__________________________________________________



(
1
,
−
2
)


image.png




__________________________________________________



(
2
,

1
)


image.png




__________________________________________________



(
0
,
−
1
)


image.png

Answer 1

Solve:
x + y = −1 => y = −1 − x
3x − y = 5 => substitute y:

3x − (−1 − x) = 5
3x + 1 + x = 5
4x + 1 = 5 → 4x = 4 → x = 1
y = −1 − 1 = −2

Solution: (1, −2). This satisfies both equations:
1 + (−2) = −1 and 3(1) − (−2) = 5.

So the correct choice is (1, −2).