Simultaneous equations: substitution
Put the expression for one unknown into the other equation, keep the bracket, isolate an unknown first, and check the answer on the graph and in both equations.
- Germany: grade 8
- Iran: grade 9
- Palestine: grade 11
- Ukraine: grade 7
Guide
A system of equations is two equations with the same unknowns. In the substitution method, write one unknown in terms of the other in one equation and put it in place of that unknown in the other equation. The second equation then has one unknown.
When we substitute an expression with several terms we put it in a bracket: with y = x - 1, 3y becomes 3(x - 1).
Choose an equation where an unknown has coefficient 1; from x + 2y = 7 we get x = 7 - 2y. When both equations give y we can set them equal.
After finding one unknown, put it into one equation to find the other. Always check in both equations. The solution is the crossing point of the two lines, which elimination also finds.