AlgebraLab

Algebra I Recipe: Solving Systems of Linear Equations Using the Multiplication-Addition Method

By G Redden

Multiplication – Addition Method
  1. Multiply one or both of the equations by some number so that one of the variables will have opposites as coefficients.
  2. Add the equations to eliminate the variable having opposites as coefficients.
  3. Solve the remaining equation for its variable.
  4. Substitute the value found in step 3 into either one of the original equations to find the value of the other variable.
  5. When adding the equations in step 2 – if both variables cancel:
    • The answer is IMS, if a true statement remains.
    • The answer is NO SOLUTION, if a false statement remains.
1.
2x - 4y = 13
4x - 5y = 8
2.
7x - 12y = -22
-3x + 8y = 18
3.
Real Life: A caterer is planning a party for 75 people. The customer has $170 to spend. A $35 pan of lasagna feeds 12 people and a $10 cheese and crackers tray feeds 9 people. How many pans of lasagna and how many cheese and crackers trays should the caterer make?
People per
pan		 * Pans of
lasagna		 + People per
tray		 * Trays of
cheese and crackers		 = People at
the party
Price per
pan		 * Pans of
lasagna		 + Price per
tray		 * Trays of
cheese and crackers		 = Money to
spend on food
Translate the problem into relationships and variables. In this case, let x equal the number of pans of lasagna and y equal the number of cheese and crackers trays
12x +   9y =   75
35x + 10y = 170