Download Solving Systems of Linear Equations

Solving Systems of Linear Equations:
Substitution Method
Tutorial 14b
3 Methods to Solve

There are 3 methods that we can use to
solve systems of linear equations.



Solve by the Graphing Method
Solve by the Substitution Method
Solve by the Addition (Elimination) Method
Substitution Method
Solve x + 3y = 7 and 2x – 4y = -6.
 Solve one equation for one variable.
 The first equation would be easiest
since the x term already has a
coefficient of one.
x + 3y = 7
-3y
-3y
x = 7 – 3y
2x – 4y = -6
equation. Then solve for y.
2(7 – 3y) – 4y = -6
 Substitute 2 for y in either one of the
14 – 6y – 4y = -6
two original equations to find the value
14 – 10y = -6
of the x coordinate.
-14
-14
x +3(2) = 7  Step 4 is to check the
2
1
-10y = -20
answer. Click here!
x+ 6 =7
y = 2
-101
x=1
1-10
 Substitute 7 –3y for x in the second
Substitution Method
Solve x + 3y = 7 and 2x – 4y = -6.
 The last step is to check your solution by
substituting both values, x = 1 & y = 2,
in both equations.
x + 3y = 7
1 +3(2) = 7
1+ 6 =7
7=7
2x – 4y = -6
2(1) – 4(2) = -6
2 – 8 = -6
-6 = -6 
The solution of the system
is (1, 2).
Substitution Method:
In Review
Steps for the Substitution Method
1. Solve one equation for one of the variables.
2. Substitute the resulting expression in the
other equation. Solve that equation.
3. Substitute the value of the variable from
step 2 in either equation. Solve the
resulting expression.
4. Check by substituting both values in both
equations.