How Do You Solve Equations By Substitution?

Substitution is one of the methods used for solving pairs of linear equations. One equation is solved for one of the variables. Then, the answer from this equation is substituted into the other equation of find the other variable.

Solve for one of the variables (x or y) in one of the equations. For example, this is a pair of linear equations: 2x+y=7 ½ and x-y=4 ½. In this case, we will solve for x in the second equation (x-y=4 ½).

X-y=4 ½x-y+y=y+4 ½ Add y to both sidesx=y+4 ½ Substitute the value of the variable (y+4 ½) that was solved for in step one into the other equation (2x+y=7 ½). 2(y+4 ½)+y=7 ½ 2y+9 +y=7 ½ 3y=-1 ½ 3y/3=1 ½(-1/3) Divide both sides by 3y=-1/2 Answer Substitute the answer in step two (y=-1/2) into the equation you solved for in step 1 (x-y=4 ½). X-y=4 ½x minus -1/2=4 ½ Subtract -1/2 from both sidesx=4The solution set is the ordered pair (x, y) or (4, -1/2).

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