ACT Preparation / Unit 9 ACT 0828 worked example, 60 to 90 seconds
Solving a System by Substitution
The idea
Substitution works best when a variable is already isolated or has a coefficient of 1, and it runs in four steps. First, solve one equation for that variable. Second, substitute the expression into the other equation, which leaves one variable. Third, solve for it. Fourth, put that value back into the expression from step one to find the other variable, then check the pair in both original equations.
In practice
Worked example: 2x + y = 11 and 5x − 3y = 22. Step one: y = 11 − 2x. Step two: 5x − 3(11 − 2x) = 22. Step three: 5x − 33 + 6x = 22, so 11x = 55 and x = 5. Step four: y = 11 − 10 = 1. Check: 10 + 1 = 11, and 25 − 3 = 22.
Where people slip
Wrap the substituted expression in parentheses. Without them, the −3 multiplies only the 11, and the answer goes wrong.
Your place on the trail
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