Solving Systems of Equations by Elimination BACK Using
Solving Systems of Equations by Elimination BACK
Using the Addition Method BACK
Using the Addition Method Finish problem by Multiply by c-2 solving for using substitution. 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… • Let p = # of pigs • Let c = # chickens • Counting Equation p + c = 30 • Value Equation 4 p + 2 c = 84 BACK
Pigs and Chickens -2 p + c = 30 4 p + 2 c = 84 -2 p – 2 c = -60 2 p = 24 p = 12 c = 18 BACK
Systems of Equations Elimination Using Addition, Subtraction, & Multiplication BACK
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