Solve the system y = x + 8 and 5x + 3y = 16

Key takeaway: Because $y$ is already isolated, the cleanest approach is substitution. This turns the system into one equation in one variable.

We solve

$y=x+8$

$5x+3y=16.$

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

$5x+3(x+8)=16.$

Distribute:

$5x+3x+24=16.$

Combine like terms:

$8x+24=16.$

Subtract 24:

$8x=-8.$

So

$x=-1.$

Now find $y$:

$y=x+8=-1+8=7.$

Therefore the solution is

$\boxed{(-1,7)}.$

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Pitfalls the pros know 👇 If you substitute correctly but forget to simplify the final $y$ value, you may lose the ordered pair. Always finish by finding both coordinates, not just one.

What if the problem changes? If the first equation were instead $y=x-8$, the same substitution method would still work, but the final ordered pair would change. The method is unchanged; only the arithmetic changes.

Tags: linear system, substitution, ordered pair