Question

Find the solution of the system of equations
-4x - y =-28
x + y=4

Answer 1

To solve the system of equations:

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

We can use the substitution or elimination method. Here, I'll use substitution. First, we can solve Equation 2 for \(y\):

\[
y = 4 - x
\]

Now we can substitute this expression for \(y\) into Equation 1:

\[
-4x - (4 - x) = -28
\]

Now, simplify this equation:

\[
-4x - 4 + x = -28
\]

Combine like terms:

\[
-3x - 4 = -28
\]

Next, add 4 to both sides:

\[
-3x = -24
\]

Now, divide by -3:

\[
x = 8
\]

Now that we have \(x\), we can find \(y\) using Equation 2:

\[
y = 4 - x = 4 - 8 = -4
\]

Thus, the solution to the system of equations is:

\[
(x, y) = (8, -4)
\]

To verify, we can substitute \(x = 8\) and \(y = -4\) back into both original equations:

1. For Equation 1:

\[
-4(8) - (-4) = -32 + 4 = -28 \quad \text{(True)}
\]

2. For Equation 2:

\[
8 + (-4) = 4 \quad \text{(True)}
\]

Since both equations hold true, the solution is confirmed as:

\[
\boxed{(8, -4)}
\]