Solve the system x = -y + 8 and 4x - 3y = -3

Key concept: This system is ideal for substitution because the first equation already isolates $x$. After substitution, solve the resulting single-variable equation and then back-substitute.

Step by step

We solve

$x=-y+8$

$4x-3y=-3.$

Substitute $x=-y+8$ into the second equation:

$4(-y+8)-3y=-3.$

Distribute:

$-4y+32-3y=-3.$

Combine like terms:

$-7y+32=-3.$

Subtract 32 from both sides:

$-7y=-35.$

So

$y=5.$

Now substitute into $x=-y+8$:

$x=-5+8=3.$

The solution is

$\boxed{(3,5)}.$

Pitfall alert

Do not forget to distribute the 4 across both terms in $4(-y+8)$. Missing that step is one of the most common algebra errors in substitution problems.

Try different conditions

If the first equation were written as $y=8-x$, the same solution would appear after substitution. Any algebraically equivalent form is valid as long as it is substituted consistently.

Further reading

substitution method, ordered pair, linear system