Solving Systems of Equations by Elimination BACK

Using the Addition Method BACK

Using the Addition Method Finish problem by solving for c using substitution. Multiply by -2 BACK

Addition Method - Seven Steps Step 1 Write both equations of the system in standard form Ax + By = C Step 2 If necessary multiply one or both equations by appropriate numbers so that the coefficients of x or y are negatives of each other. BACK

Addition Method - Seven Steps Step 3 Add the two equations to get one equation with only one variable. Step 4 Solve the equation from Step 3. Step 5 Substitute the solution from Step 4 into either of the original equations. BACK

Addition Method - Seven Steps Step 6 Solve the resulting equation from Step 5 for the remaining variable. Step 7 Check the answer. BACK

Solve. Multiply by 2 Multiply by 3 BACK

Your turn, Example Step 1 Write both equations of the system in standard form Ax + By = C BACK

Standard Form

Multiply by -2 Multiply by 3

Example Step 6 Solve the resulting equation from Step 5 for the remaining variable. BACK

Example Step 7 Check the answer. BACK

Example BACK

Using the Addition Method Multiply by -2 What does it mean? BACK

A false statement would indicate the lines of the two equation would not intersect and therefore has no solution. BACK

Addition Method Multiply by 4 Multiply by 3 What does it mean? BACK

This is a true statement, therefore the equations are the same and would make two lines that coincide with each other and produce an infinite amount of solutions BACK

Once upon a time… …a handsome math professor was in a barnyard that was full of pigs and chickens. BACK

Once upon a time… The handsome math professor counted all of the heads of the pigs and chickens. The result was 30. The handsome math professor counted all of the feet of the pigs and chickens. The result was 84. How many pigs were there? How many chickens were there?

Once upon a time… 4p + 2c = 84 Let p = # of pigs Let c = # chickens Counting Equation p + c = 30 Value Equation 4p + 2c = 84 BACK

Pigs and Chickens p + c = 30 4p + 2c = 84 -2p – 2c = -60 2p = 24 BACK

Systems of Equations Elimination Using Addition, Subtraction, & Multiplication BACK