Question

Is (
–
2,9) a solution to this system of equations?
y= -2x+5
y= 5/2x –1

Answer 1

To determine if the point \((-2, 9)\) is a solution to the system of equations, we need to substitute \(x = -2\) and \(y = 9\) into both equations and check if the equations hold true.

**First equation:**
\[ y = -2x + 5 \]
Substituting \(x = -2\):
\[
y = -2(-2) + 5 = 4 + 5 = 9
\]
So, \(y = 9\) matches, which is correct for the first equation.

**Second equation:**
\[ y = \frac{5}{2}x - 1 \]
Substituting \(x = -2\):
\[
y = \frac{5}{2}(-2) - 1 = -5 - 1 = -6
\]
Here, \(y = 9\) does not match since we got \(-6\).

Since the point \((-2, 9)\) satisfies the first equation but not the second equation, it is not a solution to the system of equations.