| Example: A caterer ia planning a party for 64 people. The customer has $150 to spend. A $39 pan of pasta feeds 14 people and a $12 sandwich tray feeds 6 people. How many pans of pasta and how many sandwich trays should the caterer make. |
Equation
1: 14p + 6s = 64 Equation 2: 39p + 12s = 150 |
| Step
1: Multiply one or both of the equations by a
constant to obtain coefficients that differ only in sign
of the variables. Step 2: Add the revised equations from Step 1. Combining like terms will eliminate one of the variables. Solve for the remaining variable. Step 3: Substitute the value obtained in Step 2 into either of the original equations and solve for the other variable. |
Step
1: 14p + 6s = 64 (-2) Step 2: -28p - 12s = -128 39p + 12s = 150 p = 2 Step 3: 14(2) + 6s = 64 28 + 6s = 64 s = 6 Solution = (2, 6) |
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