Unit 1.3

USE YOUR CALCULATOR!!!

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.

Vocabulary

Substitution method Elimination method

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.

Ex. Solve the system using the substitution method.

y + 3x = 5 Equation 1y -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)

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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

Ex. Solve the system using the elimination

method.

5x + 7y = 2450 Equation 18x + 13y = 4325 Equation 2

Step 1: Multiply 5x + 7y = 2450 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

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