Download 39) The Frosty Ice-Cream Shop sells sundaes for $2 and banana

Name___________________________ Date_____________________
per.____
REVIEW- SOLVING SYSTEMS OF LINEAR EQUATIONS
1) The local ice-cream shop sells sundaes for $3 and banana splits for $6. On a hot summer day, the
shop sold 10 more sundaes than banana splits and made $129. Which system of equations could be
used to find the number of sundaes, s, and banana splits, b, that the shop sold that day?
2) The length of a rectangle is equal to four times the width. Which system of equations can be used
to find the dimensions of the rectangle if the perimeter is 40 centimeters?
3) Lalo and Kester went to the candy store. Lalo bought 20 pieces of fudge and 2 pieces of bubble
gum for a total of $10.50. Kester was going to share his candy with a friend and bought 30 pieces of
fudge and 4 pieces of bubble gum for a total of $16.
Which system of equations could be used to determine the cost of 1 piece of fudge, f, and 1 piece
of bubble gum, g?
5
x − 3 is given below. Graph y = x − 1 on the grid.
3
MUST GRAPH WORK TO RECEIVE
FULL CREDIT EVEN WITH CORRECT
ANSWER.
4) The graph of the equation y =
What is the solution to this system of equations?
5) The equations of two lines are 3x−2 = y and y = 6x + 4. What is the value of x in the solution for
this system of equations?
6) Which of the following is the solution for
this system of linear equations?
y=−x −1
4x + 2y = 10
7) What is the y-coordinate of the solution to the system of linear equations below
6x + 4y = 4
3x − 2y = −18
8) Which of the following is the solution for this system of linear equations?
3x+3y = 6
8x −4y = 0
9) Marcos had 17 coins in nickels and quarters. The difference in nickels and quarters is 3. He wrote
a system of equations to represent this situation, letting x represent the number of nickels and y
represent the number of quarters. What is the solution?
____ 10. Tell whether the ordered pair (3, –1) is a solution of the system
.
____ 11. Solve the system
{
y = x – 1 by substitution.
y = 3x + 5
Answer:__________
____ 12. Solve the system
x = 4y – 10 by substitution.
{
x + 2y = 8
Answer:__________
_____ 13. Solve the system
{
4x + 4y = 20 by elimination.
7x + 4y = 32
Answer:__________
_____ 14. Solve the system
{
3x + 2y = −8 by elimination.
x + 4y = 4
Answer:__________
____ 15. The sum of two numbers is 100. One number is 20 less than triple the second number. Write and solve the
system.
____ 16. Solve the system
−4x + 4y = − 12 by graphing.
{
4
4 = x − 2y
____ 17. Solve the system
−x – 6y = 42 by elimination. Express your answer as an ordered pair.
{
4
5x + 6y = − 18
_____ 18. Given point (2,4) and slope −3, write the equation in slope-intercept form.
_____ 19. Find the y-intercept of 8x + 12 = − 4y.
____ 20. Joslyn is 12 years less than her brother George. The sum of their ages is 92.
What equations can you use to figure out how old the brother and sister are?
How old is Joslyn?
Joslyn is ___________.
21. Find the solution to the system of linear equations described by the tables below:
x
1
2
3
0
-1
-3
-2
y
0
1
2
-1
-2
-4
-3
x
1
2
0
-1
-2
-3
3
y
8
11
5
2
-1
-4
14
22. Find the solution to the system of linear equations described by the sets of ordered pairs listed below:
{ (-4,-5), (-2,-1), (8,19), (3,9), (1,5)} and { (1,0), (6,5),(4,3), (-4,-5),(-2,-3)}
23. Find the solution to the system of linear equations described by the sets of ordered pairs listed below:
{(-1,-2), (0,-1), (4,3),(-2,-3), (-4,-5)}
and {(2,4), (0,5), (6,2),(4,3), (-2,-6)}
24. Find the solution to the system of linear equations described in the tables below:
X
-3
-2
-1
0
1
Y
-14
-10
-6
-2
2
X
-1
0
1
-2
2
Y
-10
-2
6
-18
14
25. What is the solution to the system of equations
graphed below?
26. What is the solution for the system of equations
on the graph below?
27. What is the solution for the system of equations
graphed below?
28. What is the solution to the system of equations
graphed below?
29. What is the equation of the line PARALLEL to 2y=x+6 and goes through the point (− 4,5).
1
3
30. What is equation of line PERPENDICULAR to y   x  4 and goes through point (−2,1).
31. Find equation of the line PARALLEL to
one below and goes through the point (2, −5).
32.Find equation of line PERPENDICULAR
to one below and goes through point ( 6,0)
Answer Key
1.
10+b = s; 3s + 6b = 129; s = 21 and b = 11
2. L = 4w; 2(l+w) = 40; w=4 and l = 16
3. 20f + 2b = 10.5 and 30f + 4b = 16 ; b = .25 and f = .50
4. (3,2)
5. (-2,-8)
6. (6,-7)
7. Y = 5
8. (3,-1)
9. (10,7)
10. No
11. (-3,-4)
12. (2,3)
13. (4,1)
14. (-4,2)
15. X+y=100; x = 3y – 20; (70,30)
16. (2,-1)
17. (6,-8)
18. Y = -3x + 10
19. B = -3; (0,-3)
20. J = g – 12; j + g = 92; Joslyn is 40
21. (-3,-4)
22. (-4,-5)
23. (4,3)
24. (0,-2)
25. (4,4)
26. No solution, parallel lines
27. Infinite solutions; same line.