Question

Which of the following systems of equations has the solution
(
1
,
2
)
?

A.
{
y
−
x
=
1
3
y
−
4
x
=
10

B.
{
−
2
y
+
5
x
=
−
1
2
y
+
2
x
=
6

C.
{
3
y
+
2
x
=
8
4
y
−
x
=
7

D.
{
3
y
−
x
=
1
8
y
−
2
x
=
4

Answer 1

Plug x = 1, y = 2 into each system:

A: y − x = 2 − 1 = 1 (ok); 3y − 4x = 6 − 4 = 2 (not 10) → no.

B: −2y + 5x = −4 + 5 = 1 (not −1) → no.

C: 3y + 2x = 6 + 2 = 8 and 4y − x = 8 − 1 = 7 → both true.

D: 3y − x = 6 − 1 = 5 (not 1) → no.

So the correct system is C.