Question

Solve using system of equations

-2x+y=5
-5x+y=-4

Answer 1

To solve the system of equations:

1. \(-2x + y = 5\) (Equation 1)
2. \(-5x + y = -4\) (Equation 2)

we can use the method of elimination or substitution. Let's use substitution in this case.

1. From Equation 1, we can express \(y\) in terms of \(x\):

\[
y = 2x + 5
\]

2. Now, substitute \(y\) from Equation 1 into Equation 2:

\[
-5x + (2x + 5) = -4
\]

Simplifying this:

\[
-5x + 2x + 5 = -4
\]

\[
-3x + 5 = -4
\]

Now, isolate \(x\):

\[
-3x = -4 - 5
\]

\[
-3x = -9
\]

\[
x = 3
\]

3. Now that we have \(x\), we can substitute it back into the equation for \(y\):

\[
y = 2(3) + 5
\]

\[
y = 6 + 5
\]

\[
y = 11
\]

Thus, the solution to the system of equations is:

\[
(x, y) = (3, 11)
\]


You can verify this solution by substituting \(x\) and \(y\) back into the original equations to ensure they hold true:

For Equation 1:
\[
-2(3) + 11 = -6 + 11 = 5 \quad \text{(True)}
\]

For Equation 2:
\[
-5(3) + 11 = -15 + 11 = -4 \quad \text{(True)}
\]

Both equations are satisfied, confirming that the solution is correct.