The first equation tells you that y equals 2x−8. So, one way to start solving this system of equations is to substitute 2x−8 anywhere you see y in the second equation. Go for it. Substitute 2x−8 for y in the second equation.

Question

y= 2x−8
x= −3y+18
x = −3(
) + 1

Answer 1

Sure! Given the first equation \( y = 2x - 8 \), we can substitute \( y \) into the second equation \( x = -3y + 18 \).

So substituting \( 2x - 8 \) for \( y \) gives us:

\[ x = -3(2x - 8) + 18 \]

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

1. Distribute the -3: \[ x = -6x + 24 + 18 \]

2. Combine like terms: \[ x = -6x + 42 \]

3. Add \( 6x \) to both sides: \[ x + 6x = 42 \ 7x = 42 \]

4. Finally, divide by 7: \[ x = 6 \]

Now that we have \( x \), we can substitute it back into the first equation to find \( y \):

\[ y = 2(6) - 8 \ y = 12 - 8 \ y = 4 \]

Thus, the solution to the system of equations is \( x = 6 \) and \( y = 4 \).