Question

Determine the solution to the system of equations below.
-5x - 7y= 11
x - 2y= -9

infinitely many solutions
x= -5, y= 2
no solution
x= -5, y= -7

Answer 1

To determine the solution to the system of equations, we'll solve the given equations step by step.

The system of equations is:
1. \(-5x - 7y = 11\) (Equation 1)
2. \(x - 2y = -9\) (Equation 2)

Let's express Equation 2 in terms of \(x\) to substitute into Equation 1.

From Equation 2:
\[
x = -9 + 2y
\]
Now, we can substitute this expression for \(x\) into Equation 1.

Substituting \(x\) in Equation 1:
\[
-5(-9 + 2y) - 7y = 11
\]

Expanding this:
\[
45 - 10y - 7y = 11
\]
\[
45 - 17y = 11
\]

Now, isolate \(y\):
\[
-17y = 11 - 45
\]
\[
-17y = -34
\]
\[
y = 2
\]

Next, substitute \(y = 2\) back into Equation 2 to find \(x\):
\[
x - 2(2) = -9
\]
\[
x - 4 = -9
\]
\[
x = -9 + 4
\]
\[
x = -5
\]

So the solution to the system of equations is:
\[
x = -5, y = 2
\]

Based on the provided options, the correct answer is:
**x= -5, y= 2**