Question

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

Answer 1

To determine if the point \((-4, 2)\) is a solution to the system of equations, we need to substitute \(x = -4\) and \(y = 2\) into both equations and check if both equations are satisfied.

1. For the first equation:
\[
y = \frac{1}{4}x + 1
\]
Substituting \(x = -4\):
\[
y = \frac{1}{4}(-4) + 1 = -1 + 1 = 0
\]
But \(y\) should be \(2\), so this equation is not satisfied.

2. For the second equation:
\[
y = \frac{1}{2}x - 1
\]
Substituting \(x = -4\):
\[
y = \frac{1}{2}(-4) - 1 = -2 - 1 = -3
\]
Again, this does not satisfy \(y = 2\).

Since \((-4, 2)\) does not satisfy either equation, the answer is **no**.