3.1.2 Using Algebraic Methods to Solve Linear Systems - Worksheet
Example 1: Use substitution to solve each system of equations. 1. 2. = − y x 19 3.
4.
− = − = 2 3 2 11 x y x y 2
y x x y
x y y x
= + =− − 3 5
17 7
+ = = +
x y
3 5
2
27
− =
Example 2: Use elimination to solve each system of equations. 5. + = − − =− x y x y 2 12 5 33 6. − =− − + =− x y x y 2 5 5 2 8 58
+ = − − =− x y x y 1 2
7.
8.
+ =− − = 2 6 8 5 3 88 x y x y
4 2 2 6
Example 3: Classify each system and determine the number of solutions. 9. − =− − =− x y x y 5 3 15 3 9 10. − =− = − x y x y 2 8 4 8 56 11. + = + =− x y x y 8 12 60 2 3 24
− =− x y 1 3 2 6 2 12 − =− x y
12.
Example 4: 13. Denise owns a car that runs on a mixture of gasoline and ethanol. She can buy fuels that have 85% ethanol or 25% ethanol. How much of each type of fuel should she buy if she wants to fill her 20 gal tank with a mixture of fuel that contains 50% ethanol?
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