Question

Is (
–
2,
–
7) a solution to this system of equations?
10x–5y=15
3x–8y=
–
50

Answer 1

To determine if \((-2, -7)\) is a solution to the system of equations, we will substitute \(x = -2\) and \(y = -7\) into both equations and check if they hold true.

1. **Substituting into the first equation:**
\[
10x - 5y = 15
\]
\[
10(-2) - 5(-7) = 15
\]
\[
-20 + 35 = 15
\]
\[
15 = 15 \quad \text{(True)}
\]

2. **Substituting into the second equation:**
\[
3x - 8y = -50
\]
\[
3(-2) - 8(-7) = -50
\]
\[
-6 + 56 = -50
\]
\[
50 = -50 \quad \text{(False)}
\]

Since the second equation does not hold true with the values \(-2\) for \(x\) and \(-7\) for \(y\), the point \((-2, -7)\) is **not** a solution to the system of equations.