Question

Is (5,2) a solution to this system of equations?
5x–4y=–20
7x–10y=15

Answer 1

To determine if \((5, 2)\) is a solution to the given system of equations, we substitute \(x = 5\) and \(y = 2\) into both equations.

1. For the first equation:
\[
5x - 4y = -20
\]
Substitute \(x = 5\) and \(y = 2\):
\[
5(5) - 4(2) = -20
\]
\[
25 - 8 = -20
\]
\[
17 \neq -20
\]
Thus, \((5, 2)\) does not satisfy the first equation.

Since the point does not satisfy the first equation, it cannot be a solution to the system of equations.

You can check the second equation as well for completeness.

2. For the second equation:
\[
7x - 10y = 15
\]
Substitute \(x = 5\) and \(y = 2\):
\[
7(5) - 10(2) = 15
\]
\[
35 - 20 = 15
\]
\[
15 = 15
\]
This equation is satisfied.

However, since \((5, 2)\) does not satisfy the first equation, we can conclude that \((5, 2)\) is **not** a solution to the system of equations.