Question

Is (7, 3) the solution to the system of these linear equations: 3x+2y=5 and −x+6y=11 ? Why?

No, because the graphs don’t intersect at (7, 3)

No, because the graphs intersect at (7, 3)

Yes, because the graphs don’t intersect at (7, 3)

Yes, because the graphs intersect at (7, 3)
.

Answer 1

To determine whether (7, 3) is a solution to the system of equations, we will substitute \(x = 7\) and \(y = 3\) into both equations and see if both equations are satisfied.

1. For the first equation:
\[
3x + 2y = 5
\]
Substitute \(x = 7\) and \(y = 3\):
\[
3(7) + 2(3) = 21 + 6 = 27
\]
This does not equal 5. So (7, 3) is not a solution to the first equation.

2. For the second equation:
\[
-x + 6y = 11
\]
Substitute \(x = 7\) and \(y = 3\):
\[
-7 + 6(3) = -7 + 18 = 11
\]
This does equal 11, so (7, 3) is a solution to the second equation.

Since (7, 3) does not satisfy the first equation, it is not a solution to the system of equations.

**Therefore, the correct answer is:**
**No, because the graphs don’t intersect at (7, 3)**.