Question

4x - y = 20 y equals negative x + 5

Answer 1

To solve the system of equations given by:

1. \( 4x - y = 20 \)
2. \( y = -x + 5 \)

we can use the substitution method since the second equation is already solved for \(y\).

### Step 1: Substitute \(y\)

Substitute \(y\) from the second equation into the first equation:

\[
4x - (-x + 5) = 20
\]

### Step 2: Simplify

This simplifies to:

\[
4x + x - 5 = 20
\]

Combine like terms:

\[
5x - 5 = 20
\]

### Step 3: Solve for \(x\)

Add 5 to both sides:

\[
5x = 25
\]

Now divide by 5:

\[
x = 5
\]

### Step 4: Substitute back to find \(y\)

Now substitute \(x = 5\) back into the second equation to find \(y\):

\[
y = -5 + 5
\]

So,

\[
y = 0
\]

### Conclusion

The solution to the system of equations is:

\[
(x, y) = (5, 0)
\]