2 Unit 1 – Algebra: Linear Systems, Matrices, & Vertex-Edge Graphs 1.3 – Solve Linear Systems AlgebraicallyGeorgia Performance Standard:MM3A5c – Represent and solve realistic problems using systems of linear equations.
4 So what’s up with the Substitution Method? Step 1:Solve one of the equations for one of it’s variablesStep2:Plug in what you found into the other equationStep 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 1y -2x = -5 Equation 2Step 1: Solve Equation 2 for yy= 2x - 5Step 2: Substitute result for y into Equation 1 & solve(2x-5) + 3x = 5x= 2Step 3: Plug the value of x into the revised Equation from Step 1 and solve for y.y= 2(2) – 5y= -1Solution: (2,-1)
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 variablesStep2:Add revised equations from Step 1 and solve for remaining variableStep 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 18x + 13y = Equation 2Step 1: Multiply5x + 7y = multiply by -88x + 13y = 4325 multiply by -5y= 225Step 2: Substitute result for y into one of the original equations5x + 7(225) = 2450x= 175X = 175, Y = 225