To solve the system of equations
- \(-2x + 4y = 56\)
- \(x + 5y = 28\)
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:
\[ \boxed{(-12, 8)} \]