Question

Is (−2, 6)
(
−
2
,

6
)
a solution to the system of these linear equations: x+2y=10
𝑥
+
2
𝑦
=
10
and 3x+y=0
3
𝑥
+
𝑦
=
0
? Why?

Answer 1

Yes. A point is a solution to a system if it satisfies both equations. Substitute x = −2, y = 6:

x + 2y = −2 + 2(6) = −2 + 12 = 10 ✓
3x + y = 3(−2) + 6 = −6 + 6 = 0 ✓

Both equations hold, so (−2, 6) is a solution.