Question

Is (6,4) a solution to this system of equations?
y=2x–8
y=–1/3 x+6
yes or no

Answer 1

To determine if (6, 4) is a solution to the system of equations, we need to substitute \(x = 6\) and \(y = 4\) into both equations and check if they hold true.

1. For the first equation:
\[
y = 2x - 8
\]
Substituting \(x = 6\) and \(y = 4\):
\[
4 = 2(6) - 8
\]
\[
4 = 12 - 8
\]
\[
4 = 4 \quad \text{(True)}
\]

2. For the second equation:
\[
y = -\frac{1}{3}x + 6
\]
Substituting \(x = 6\) and \(y = 4\):
\[
4 = -\frac{1}{3}(6) + 6
\]
\[
4 = -2 + 6
\]
\[
4 = 4 \quad \text{(True)}
\]

Since (6, 4) satisfies both equations, the answer is **yes**.