PRECALCULUS TEST REVIEW
Systems of Equations
Determine whether each ordered pair is a solution of the system of equations.
⎧4 x − y = 1
⎪
1. ⎨
⎪6 x + y = −6
⎩
Solve the system by graphing.
⎧2 x + y = 6
2. ⎨
⎩− x + y = 0
3.
⎧x − y = 0
⎨ 2
⎩x − y = 2
a) (0,− 3)
b) (−1,− 4)
⎛ 3
⎞
c) ⎜ − , − 2 ⎟
⎝ 2
⎠
⎛ 1
⎞
d ) ⎜ − , − 3⎟
⎝ 2
⎠
Solve each system by substitution.
⎧x − y = 0
4. ⎨
⎩5 x − 3 y = 10
⎧6 x − 3 y − 4 = 0
5. ⎨
⎩x + 2 y − 4 = 0
⎧x2 − y = 0
6. ⎨
⎩2 x + y = 0
⎧ x − y = −1
7. ⎨ 2
⎩ x − y = −4
Solve the system by elimination.
⎧x + 2 y = 4
8. ⎨
⎩x − 2 y = 1
⎧9 x + 3 y = 1
9. ⎨
⎩3x − 6 y = 5
⎧2 x + 3 y = 18
10. ⎨
⎩5 x − y = 11
⎧3x + 11 y = 4
11. ⎨
⎩− 2 x − 5 y = 9
Set up and solve the system using a method of your choice.
12. The weekly rentals for a newly released DVD of an animated film at a local video
store decreased each week. At the same time, the weekly rentals for a newly
released DVD of a horror film increased each week. Models that approximate the
weekly rentals R for each DVD are
⎧ R = 360 − 24 x
⎨
⎩ R = 24 + 18 x
where x represents the number of weeks each DVD was in the store, with x=1
corresponding to the first week.
a) After how many weeks will the rentals for the two movies be equal?
13. The perimeter of a rectangle is 280 centimeters and the width is 20 centimeters
less than the length. Find the dimensions of the rectangle.
14. An airplane flying into a headwind travels the 1800-mile flying distance between
Pittsburg, Pennsylvania and Phoenix, Arizona in 3 hours and 36 minutes (3.6
hours). On the return flight, the distance is traveled in 3 hours. Find the airspeed
of the plane and the speed of the wind, assuming that both remain constant.
15. At a local high school city championship basketball game, 1435 tickets were sold.
A student admission ticket cost $1.50 and an adult admission ticket cost $5.00.
The sum of all the total ticket receipts for the basketball game were $3552.50.
How many of each type of ticket were sold?