Two equations, two letters, and one pair of numbers that satisfies both. These free printable worksheets practice getting from two unknowns down to one.
Both methods on these sheets do the same thing, and a child who sees that has understood the topic. Two equations with two unknowns cannot be solved as they stand, so the first move is always to produce one equation with one unknown. Elimination cancels a letter by adding the equations; substitution replaces a letter with what it already equals. After that step, both are an equation the child has already met.
Why this sheet works
Adding two equations together is the part that looks like a trick, and it is not. Both sides of each equation are equal, so adding the left of one to the left of the other — and the right to the right — keeps the balance. It is the same move as adding 3 to both sides, done with a whole equation instead of a number.
How this one works
One question from this sheet, worked through a step at a time.
y = −3x − 12 3x + 4y = −3
y = −3x − 12
3x + 4y = −3
3x + 4y = −3
3x + 4(−3x − 12) = −3
3x + 4(−3x − 12) = −3
x=−5
x=−5
y=3
x = −5andy = 3
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 = −5.
Half done — and stopping here is the usual way to lose the other half. Put x back into the first equation: y = −3(−5) − 12 = 3.
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 (−5, 3).
