Substitution rearranges one equation for a single letter and puts that expression into the other. These free printable worksheets give pairs where one equation is already close to that form.
If y = 2x + 1, then every y in the other equation can be replaced by 2x + 1. What comes out is one equation in one letter, which is something already familiar. The method is longer to write than elimination and shorter to understand, and it is the one that generalises to everything that comes after.
Why this sheet works
Brackets are the thing to insist on. Substituting 2x + 1 into 3y means 3(2x + 1), and a child who writes 3 × 2x + 1 has lost a term before starting. Writing the bracket every time, even where it turns out not to matter, is the habit that prevents it.
How this one works
One question from this sheet, worked through a step at a time.
y = x + 8 x − 10y = 10
y = x + 8
x − 10y = 10
x − 10y = 10
x − 10(x + 8) = 10
x − 10(x + 8) = 10
x=−10
x=−10
y=−2
x = −10andy = −2
Two equations, two letters. Neither one can be solved on its own — so the first move, whichever method you use, is to get down to ONE equation with ONE letter in it.
The first equation already says what y IS. So wherever the second equation has a y, that whole expression can go in its place — which leaves only x.
Now it is an equation you have already met: multiply out, collect the x terms, and solve. That gives x = −10.
Half done — and stopping here is the usual way to lose the other half. Put x back into the first equation: y = (−10) + 8 = −2.
Check the pair in the equation you did NOT use to find it — that is the only check that catches a slip in the middle. The solution is (−10, −2).
