Download Math 10 Academic: Linear Review

Name: _____________
Math 10 Academic: Linear Review
1. Solve the following system of equations as specified:
a. Graphically
2x - y = -1
3x + 2y = 16
2x + y = 5
-3x + 2y = -4
3x - 4y = 10
2x + 3y = 1
b. Elimination
x=3
3x - 2y = 11
y = 3x - 8
2x - y = 5
2a - 3b = 9
a = -6 - 2b
c. Substitution
x - y = 12
x + y = -2
3x - y = 16
2x + 3 = y + 16
x - 2y = 2
2x - 3y = 9
2. Put into y = mx + b form
a. x = 2y - 11
b. 3x + 2y = 4
c. 2x + 0.75y = 330
3. A Porsche travelled 1.6 times as fast as a BMW. The difference in their speeds were
45km/h. Find the speed of each car
4. Express x in terms of y
a. 3x + y = 4
b. 2x = y + 4
c. 3x = 4 - y
5. If lines 2x - 3y = 0 and 3x - 2y + 10 intersect at P and lines 6x - y + 1 = 0 and x + 3y
+ 16 = 0 intersect at Q, determine the midpoint of PQ
6. Brayden collected 70 coins consisting of quarters and nickels. The total value of the
coins is $9.50, how many of each type of coin does he have?
7. Solve this system of equation: y +
3
x = -1
4
and
x-
1
y=5
4
8. The book store cash register had $66 in $2 bills and $5 bills. There were three times as
many $2 bills as $5 bills, how many of each were there?
9. Find the points of the vertices of the triangle
A
4x+y=18
3x-8y=-39
C
B
x+2y=1
Name: _____________
10. Alex purchased 5 boxes of chocolates and 3 bags of candies for $12.05. If the cost of a
box of chocolates and a bag of candies were reversed then it would cost Lindsay $11.07
for the same order. What is the cost of a box of chocolates?
11. The sum of the digits of a two digit number is 14. When 18 is added to the number, the
digits are reversed. Find the number
12. Brass is a mixture of copper and zinc. A brass bloc containing 60% Zinc and a brass bar
containing 40% Zinc are melted together. The result is a mixture of 51% zinc. If 400kg
of the new mixture is obtained, what was the original mass of the block?
13. If 1 is added to the numerator and denominator of a fraction, the result is equivalent to
1/3. If 9 is subtracted from the denominator of the original fraction, the result is 1/2.
What was the original fraction?
14. At a sale, all records are one price and 8-tracks are another. Matt bought the records
for $9.99 each and the 8-tracks for $2.59 each. He spent total of $160.95 and bought a
total of 25 items. How many of each did he buy?
15. Ian has $12.80 in his pocket consisting of nickels and quarters. He has ten more nickels
than quarters. How many of each does he have?
16. Confirm or deny if the ordered pair (3 , -5) is the solution to the linear system defined
by:
2x + 5y = -19 and 3y - 4x = -27
17. The Beyonders Club held a car wash to raise money. They washed cars for $5 each and
vans for $10 each. They washed 76 vehicles and earned $580. How many of each type
of vehicle did they wash?
18. Daniel had $10 000 to invest. He invested part in a term deposit paying 4% per annum
and the remainder in bonds paying 5% per annum. If the total interest after one year
was $440, how much did he invest at each rate?
19. Describe the graph of a system of equations, which have no solutions.

Name: _____________
b. (3, 1), (3, 1), (0,-3)
1
11
y = x+
b. y = 2x - 4
2
2
c. (5, -7), (3, -7), (12, 5)
2.
c. y = -3x + 4
1
4
1
1
4
4. x = - y +
b. x = y + 2 c. x = - y +
3
3
2
3
3
5. (-3.5, -4.5) 6. 40 nickels, and 30 quarters 7. (4, -4) 8. 18 $2 bills and 6 $5 bills
3. Porsche = 120km/h and BMW = 75km/h
9. A(3, 4) B(5, -2)
$1.20 per box
C(-5, 3)
10. Chocolates are $1.69 per box and candies are
11. a is 6 and b is 8. The numbers are 68 and 86
40% zinc
13. 7 over 23 is the fraction
nickels
12. 220kgof 60% zinc and 180kg of
14. 13 records and 12 8-tracks 15. 41 quarters and 51
16. yes 17. 40 vans and 36 cars 18. 6000 in 4% and 4000 in 5%
they never
intersect and have no common points.
19. They are parallel,