Question

GG.1 Is (x, y) a solution to the system of equations?
N46
Is (3,
–
4) a solution to this system of equations?
5x+2y=7
8x+5y=4

Answer 1

To determine if the point (3, -4) is a solution to the system of equations, we need to plug the values of \(x = 3\) and \(y = -4\) into both equations and see if they hold true.

1. **First Equation:**
\[
5x + 2y = 7
\]
Substitute \(x\) and \(y\):
\[
5(3) + 2(-4) = 7
\]
Calculate:
\[
15 - 8 = 7
\]
\[
7 = 7 \quad \text{(True)}
\]

2. **Second Equation:**
\[
8x + 5y = 4
\]
Substitute \(x\) and \(y\):
\[
8(3) + 5(-4) = 4
\]
Calculate:
\[
24 - 20 = 4
\]
\[
4 = 4 \quad \text{(True)}
\]

Since both equations are satisfied, (3, -4) is indeed a solution to the system of equations.