Question

Is (7, 3)
(
7
,

3
)
the solution to the system of these linear equations: 3x+2y=5
3
𝑥
+
2
𝑦
=
5
and −x+6y=11
−
𝑥
+
6
𝑦
=
11
? Why?

Answer 1

No. A solution must satisfy both equations.

Check (x,y) = (7,3):
- 3x + 2y = 3(7) + 2(3) = 21 + 6 = 27 ≠ 5, so it does not satisfy the first equation.
- It does satisfy the second: −x + 6y = −7 + 18 = 11.

Therefore (7,3) is not a solution to the system. The actual solution is found by solving
x = 6y − 11 (from −x + 6y = 11). Substituting into 3x + 2y = 5 gives
3(6y−11) + 2y = 5 → 20y = 38 → y = 19/10, x = 6(19/10) − 11 = 2/5.
So the system’s solution is (x,y) = (2/5, 19/10).