Question

GG.1 Is (x, y) a solution to the system of equations?
N46
Is (
–
4,4) a solution to this system of equations?
y=
–
1
4
x+3
y=x+9

Answer 1

To determine whether the point \((-4, 4)\) is a solution to the given system of equations, we need to substitute \(x = -4\) and \(y = 4\) into each equation and check if both equations hold true.

The system of equations is:

1. \(y = -\frac{1}{4}x + 3\)
2. \(y = x + 9\)

**Check the first equation:**

Substituting \(x = -4\) into the first equation:
\[
y = -\frac{1}{4}(-4) + 3
\]
\[
y = 1 + 3
\]
\[
y = 4
\]

This matches the \(y\)-value provided, so \((-4, 4)\) satisfies the first equation.

**Check the second equation:**

Substituting \(x = -4\) into the second equation:
\[
y = -4 + 9
\]
\[
y = 5
\]

This does not match the \(y\)-value provided (which is \(4\)). Thus, \((-4, 4)\) does not satisfy the second equation.

**Conclusion:**
The point \((-4, 4)\) is not a solution to the system of equations because it does not satisfy both equations.