Question

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

Answer 1

To determine if the point \((7, -2)\) is a solution to the system of equations, we'll substitute \(x = 7\) and \(y = -2\) into each equation.

The system of equations is:
1. \(x - 5y = -3\)
2. \(y = -2\)

### Check the second equation first:
Substituting \(y = -2\) into the second equation:
\[
y = -2
\]
This is true, so \((7, -2)\) satisfies the second equation.

### Now check the first equation:
Substituting \(x = 7\) and \(y = -2\) into the first equation:
\[
7 - 5(-2) = -3
\]
Calculating the left side:
\[
7 - 5(-2) = 7 + 10 = 17
\]
Now we compare:
\[
17 \neq -3
\]
Thus, the first equation is not satisfied.

### Conclusion:
Since \((7, -2)\) does not satisfy the first equation, \((7, -2)\) is **not** a solution to the system of equations.