Transcript Solving Systems of Linear Equations by Substitution

Solving Systems of Linear
Equations by Substitution
What is Substitution?

Substitution is when you replace one
thing with another thing.

Substitution is ideal to use if one of the
variables has already been isolated in
the original system of equations.
Example:
y = -2x + 3
Example 1
Solve the following system of linear equations
using substitution.
x + y = 56
(1)
y = 7x + 8
(2)
From (2) substitute y = 7x + 8 into equation (1).
x + 7x + 8 = 56
8x + 8 = 56
8x = 48
x=6
Example 1
Substitute x = 6 into equation (1)
x + y = 56
6 + y = 56
y = 50
Check solution x = 6 and y = 50 in equation (2)
y = 7x + 8
50 = 7(6) + 8
50 = 42 + 8
50 = 50
LS = RS
Since LS = RS, solution set = {(6,50)}
Example 2
3x – y = 26
(1)
4x + 5y = 3
(2)
 Since no variables are isolated, we need to isolate one
before we can substitute.
3x – y = 26
-y = -3x + 26
y = 3x – 26
Example 2
Substitute into y = 3x – 26 into (2). Substitute x = 7 into (1).
4x + 5y = 3
4x + 5(-26 + 3x) = 3
4x – 130 15x = 3
19x – 130 = 3
19x = 133
x=7
3x – y = 26
3(7) – y = 26
21 – y = 26
–y=5
y = -5
Example 2
Check solution x = 7 and y = -5 into (2)
4(7) + 5(-5) = 3
28 – 25 = 3
3=3
LS = RS
Therefore, since LS = RS the solution set = {(7,50)}