Systems by substitution, step by step
Substitution rearranges one equation for a single letter and puts that expression into the other.
y = 4x − 1 −6x − y = 1
- 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 = 0.
- Half done — and stopping here is the usual way to lose the other half. Put x back into the first equation: y = 4(0) − 1 = −1.
- 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 (0, −1).
How it works.
- 01
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.
- 02
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.
- 03
Now it is an equation you have already met: multiply out, collect the x terms, and solve. That gives x = 0.
- 04
Half done — and stopping here is the usual way to lose the other half. Put x back into the first equation: y = 4(0) − 1 = −1.
- 05
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 (0, −1).