Ewwwww....It's a linear combonation.....GET IT OFF... GET IT OFF!!!!
| Solving a linear system using the linear combonation method. | 2x - 4y = 13
......Equation 1 4x - 5y = 8 ........Equation 2 |
| Multiply the first equation by -2 so that the x-coefficients differ only in sign. | 2x - 4y = 13
.......*-2.....-4x + 8y = -26 4x - 5y = 8 ......................4x - 5y = 8 |
| Add the resolved equations and solve for y. | ................................................3y
= -18 ...................................................y = -6 |
| Substitute the value of y into one of the origional equations. Solve for x. | 2x - 4y =
13..........................Write equation 1 2x - 4(-6) = 13
...................Substitute -6 for y. 2x + 24 =
13........................Simplify x = -11/2..................................Solve for x |
| The solution is (-11/2,-6) |  |
Now lets do a word problem
A caterer is planning a party for 64 people. The customer has $150 to spend. A $39 pan of pastta 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?
| Find the equations | 14p + 6s =
64........people at the party 39p + 12s= 150.....Money to spend on the food |
| Multiply | 14p + 6s =
64.........*-2..........-28 - 12s = -128 3p + 12s = 150.....................39p + 12s = 150 |
| Add and solve for P | ......................................................
11p = 22 ...........................................................p = 2 |
| Substitute | 14p + 6s = 64 14(2) + 6s = 64 28 + 6s = 64 s=6 |
| The caterer therefore should make 2 pans of pizza and 6 sandwich trays for the party. |