Question

Is (5,−1)
(
5
,
−
1
)
a solution to the system of these linear equations: x+y=4
𝑥
+
𝑦
=
4
and 2x+3y=7
2
𝑥
+
3
𝑦
=
7
? Why?

Answer 1

Yes. A solution to a system must satisfy each equation. Substitute x = 5, y = −1:

x + y = 5 + (−1) = 4 ✔
2x + 3y = 2(5) + 3(−1) = 10 − 3 = 7 ✔

Both equations are true, so (5, −1) is a solution (it is the intersection point of the two lines).