1. Unit 1.3
USE YOUR CALCULATOR!!!

2. Unit 1 – Algebra: Linear Systems, Matrices, & Vertex-Edge Graphs
1.3 – Solve Linear Systems Algebraically
Georgia Performance Standard:
MM3A5c – Represent and solve realistic problems using systems of linear equations.

3. Vocabulary
Substitution method
Elimination method

4. So what’s up with the Substitution Method?
Step 1:
Solve one of the equations for one of it’s variables
Step2:
Plug in what you found into the other equation
Step 3:
Substitute what you got from Step 2 into either of the original equations and solve for the other variable.

5. Ex. Solve the system using the substitution method.
y + 3x = 5 Equation 1
y -2x = -5 Equation 2
Step 1: Solve Equation 2 for y
y= 2x - 5
Step 2: Substitute result for y into Equation 1 & solve
(2x-5) + 3x = 5
x= 2
Step 3: Plug the value of x into the revised Equation from Step 1 and solve for y.
y= 2(2) – 5
y= -1
Solution: (2,-1)

6. Try These…
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7. So what’s up with the Elimination Method?
Step 1:
Multiply one or both of the equations by a constant to get coefficients that differ only in sign for one of the variables
Step2:
Add revised equations from Step 1 and solve for remaining variable
Step 3:
Substitute the value from Step 2 into either of the original equations and solve for the other variable

8. Ex. Solve the system using the elimination method.
5x + 7y = Equation 1
8x + 13y = Equation 2
Step 1: Multiply
5x + 7y =  multiply by -8
8x + 13y = 4325  multiply by -5
y= 225
Step 2: Substitute result for y into one of the original equations
5x + 7(225) = 2450
x= 175
X = 175, Y = 225

9. Try These…
Page 14: 6 & 7