Name_________________________________ Block:____ Date:__________
STUDY GUIDE
Study Guide: Unit 2C Linear Systems
Solve the linear system by graphing.
1.
3x  6 y  18
4 x  2 y  10
2.
5 x  y  9
y  2 x  2
3. Tell whether the ordered pair (4,-1) is a solution of the linear system.
4. Tickets for a school play cost $4 for adults and $2
for students. At the end of the play, the school sold
a total of 105 tickets and collected $360. Find the
number of adult tickets sold and the number of
student tickets sold.
x  2y  2
x  2y  6
5. The length of a rectangle is 2 cm more than
three times the width. If the perimeter of the
rectangle is 20 cm, what are its dimensions?
6. You can work a total of no more than 36 hours
per week at your two jobs. Housecleaning pays $5
per hour, and your sales job pays $11 per hour. You
need to earn at least $266 per week to cover your
expenses. Write a system of inequalities that shows
the various numbers of hours you can work at each
job.
7. The sum of the ages of Petra and her mother
is 53. Her mother is 11 years more than twice as
old as Petra. How old are Petra and her mother?
Solve the linear system of equations.
8. 3x – 2y = 6
4y = –8
9. 3y = -4x +4
–8x – 6y = –8
10. 4x + 5y = 18
3x – 9y = –12
11. 5y + 2x = 5x + 1
3x – 2y = 3 + 3y
12. 3x + 2y =4
2y=8-5x
13. 2x + 9y = 16
5x = 1 – 3y
14. 3x – 4y = 8
15.
5x + 3 = –7
x y 0
1
1
x y 2
2
2
16.
9 x  21y  123
15 x  35 y  205
Graph the system of linear inequalities.
20.
x y 3
y  x  2
x3
21. y  1
y  x
22.
3x  3 y  3
y  x3