Question

The first equation tells you that y equals 4x−5. So, one way to start solving this system of equations is to substitute 4x−5 anywhere you see y in the second equation. Go for it. Substitute 4x−5 for y in the second equation.
y= 4x−5
x= −6y+20
x = −6(
) + 20

Answer 1

To substitute \( y = 4x - 5 \) into the second equation \( x = -6y + 20 \), we replace \( y \) in the second equation with \( 4x - 5 \):

\[
x = -6(4x - 5) + 20
\]

Now, let's simplify this equation step by step:

1. Distribute \(-6\) inside the parentheses:
\[
x = -24x + 30 + 20
\]

2. Combine like terms:
\[
x = -24x + 50
\]

3. Add \( 24x \) to both sides to get all \( x \) terms on one side:
\[
x + 24x = 50
\]
\[
25x = 50
\]

4. Divide both sides by \( 25 \):
\[
x = 2
\]

Now that we have the value of \( x \), we can find \( y \) using the first equation \( y = 4x - 5 \):

\[
y = 4(2) - 5
\]
\[
y = 8 - 5
\]
\[
y = 3
\]

Thus, the solution to the system of equations is:
\[
(x, y) = (2, 3)
\]