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.

Question

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: \[ (x, y) = (2, 3) \]