Unit 1.3 USE YOUR CALCULATOR!!! MM3A5c

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. MM3A5c

Vocabulary  Substitution method  Elimination method MM3A5c

Substitution Method  Step 1:  Solve one of the equations for one of it’s variables (x or y…Your choice!)  Step2:  Plug in what you found (or substitute) 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. MM3A5c

 Ex. 1  Solve the system using the substitution method. 6x + 3y = 12Equation 1 3x + y = 5Equation 2 MM3A5c

Try These…  Page 13: 1-3  Use the Substitution Method MM3A5c

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 MM3A5c

 Ex. 2  Solve the system using the elimination method. 5x + 7y = 2450Equation 1 8x + 13y = 4325Equation 2 MM3A5c

Use the Elimination Method… 1.)2.) 2x + 4y = -42x + y = -3 x – 2y = 10-6x – 4y = 0 MM3A5c

Linear Systems with many or no solutions 9x – 3y = 6 3x – y = 2 MM3A5c

Linear Systems with many or no solutions x – 2y = 5 4x – 8y = 3 MM3A5c

Homework  Page 15:  1-3 (Use the Substitution Method)  7-9 (Use the Elimination Method)  15, 19, & 21 (Use either the Substitution or Elimination Method)  Make sure to show your work and circle your answers! MM3A5c