Section 7.3
Date:________________
Solving Systems by Linear Combination
Linear Combination: _________________ the equations of two lines together
so that __________________________________________.
To use linear combination to solve:
1. ____________________ the equations with like terms __________________.
2. _______________ one or both equations by a number to obtain ____________
__________________________________________ for one of the variables.
3. _____________ the equations together. (One variable should cancel!)
_____________ for the remaining variable.
4. __________________ the value into one of the original equations and
_______________ for the other variable.
5. _________________ the solution in each of the original equations __________.
Ex 1
Solve using linear combination.
-x + 2y = -8
x + 6y = -16
Check:
___________ is the solution, the point of intersection.
Ex 2 Solve using linear combination.
Multiply the ___________ equation by _________ to make the _____-term cancel.
5x - 4y = 3

_____________________________
2x + 8y = -2

_____________________________
Check:
__________ is the solution, ________________________________
Ex 3 A landscape designer uses two types of gravel for walkways. The larger gravel
weighs an average of 40 pounds per cubic foot and the smaller weighs an average of
48 pounds per cubic foot. His truck can carry a 12-cubic foot load of gravel that
weighs 520 pounds. How many cubic feet of each type can the truck carry in its bed?
Total weight:_______________________________  ____________________
Total volume (in cubic feet):____________________  ____________________
The truck is carrying _______ of the larger gravel and ______of the smaller gravel.