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We want to solve the following system of linear equations by substitution. ${x=10−3yy=x−2 (I)(II) $ When solving a system of equations using substitution, there are three steps.

- Isolate a variable in one of the equations.
- Substitute the expression for that variable into the other equation and solve.
- Substitute this solution into one of the equations and solve for the value of the other variable.

$y=x−2$

Substitute$x=10−3y$

$y=10−3y−2$

SubTermSubtract term

$y=8−3y$

AddEqn$LHS+3y=RHS+3y$

$4y=8$

DivEqn$LHS/4=RHS/4$

$y=2$

b

$2x−2y=12$

Substitute$x=5$

$2⋅5−2y=12$

MultiplyMultiply

$10−2y=12$

SubEqn$LHS−10=RHS−10$

$-2y=2$

DivEqn$LHS/-2=RHS/-2$

$y=-1$