Download Steps to Solve a System of Equations by Substitution

Steps to Solve a System of Equations by Substitution
1.
2.
3.
4.
Solve one equation for one of the variables.
Substitute the resulting expression in the other equation.
Solve the resulting equation for the first variable.
Find the values of the variables by substituting the solution back
into the original equation to solve for the second variable.
5. Check the solution in both equations of the system.
Example
-x + 2y = 4
5x –3y = 1
Step 1
Since the first equation has a term with a coefficient of -1 or 1, solve the first
equation for x
-x +2y -2y = 4 -2y
(subtract 2y from both sides)
-x = 4 -2y (result after subtracting 2y from both sides)
-x/-1 = (4 -2y)/-1 (divide both sides by -1 so x is positive)
X = 2y -4 (flipped the order of the terms)
Step 2 (substitute for x)
5(2y –4) – 3y = 1
(Substitute the resulting expression into the other equation)
Step 3 (solve for y)
10y -20 -3y = 1 (distribute the 5)
7y -20 = 1 (combine like terms)
7y -20 +20 = 1 +20 (add 5 to both sides)
7y = 21
7y/7 = 21/7 (divide both sides by 7)
y=3
Step 4 (solve for x)
-x + 2y = 4 (original equation)
-x + 2(3) = 4 (y value substituted into the equation)
-x + 6 = 4
-x +6 – 6 = 4 -6 (subtract 6 from both sides)
-x = -2 (combine like terms)
-x/-1 = -2/-1 (divide both sides by -1)
X=2
Step 5 (check your answer)
-x + 2y = 4
-(2) + 2(3) = 4
-2 + 6 = 4
4=4
5x –3y = 1
5(2) -3(3) = 1
10 -9 = 1
1=1
(Results of substituting the solutions into both equations)
Sample Systems to Solve
5x –y = 1
3x + 2y = 13
r=5–s
2r + 7s = 0
4a + b – 8 = 0
5a + 3b – 3 = 0