Solve the system x = 8y and x - 4y = 12

Key takeaway: This is a substitution problem. Since one equation already gives $x$ in terms of $y$, plug that expression into the other equation and solve for the variables.

We solve the system

$x=8y$

$x-4y=12.$

Because the first equation already gives $x$, substitute it into the second equation:

$8y-4y=12.$

Combine like terms:

$4y=12.$

So

$y=3.$

Now substitute back into $x=8y$:

$x=8(3)=24.$

The solution is

$\boxed{(24,3)}.$

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Pitfalls the pros know 👇 When one equation is already solved for a variable, do not start over with elimination unless you need to. Substitution is faster and reduces arithmetic mistakes. Also, always check the ordered pair in both equations if the problem is part of a set.

What if the problem changes? If the first equation were written as $y=\frac{x}{8}$ instead, the same substitution method would still work. If coefficients change, the solution point changes, but the process stays the same: isolate one variable, substitute, solve, then back-substitute.

Tags: substitution method, ordered pair, system of equations