Question

Solve the system of equations:
-2x+4y=56
x+5y=28

Answer 1

To solve the system of equations

1. \(-2x + 4y = 56\)
2. \(x + 5y = 28\)

we can use the substitution or elimination method. Let's use substitution here.

First, we can solve the second equation for \(x\):

\[
x = 28 - 5y
\]

Now, substitute this expression for \(x\) into the first equation:

\[
-2(28 - 5y) + 4y = 56
\]

Distribute \(-2\):

\[
-56 + 10y + 4y = 56
\]

Combine like terms:

\[
-56 + 14y = 56
\]

Now, add 56 to both sides:

\[
14y = 112
\]

Divide by 14:

\[
y = 8
\]

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

\[
x = 28 - 5(8)
\]
\[
x = 28 - 40
\]
\[
x = -12
\]

Thus, the solution to the system of equations is:

\[
\boxed{(-12, 8)}
\]

To verify, we can substitute \(x = -12\) and \(y = 8\) back into both original equations.

For the first equation:

\[
-2(-12) + 4(8) = 24 + 32 = 56 \quad \text{(True)}
\]

For the second equation:

\[
-12 + 5(8) = -12 + 40 = 28 \quad \text{(True)}
\]

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

\[
\boxed{(-12, 8)}
\]