Solve the system of equations:

-2x+4y=56
x+5y=28

1 answer

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:

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