Solving Linear Systems – Test Review
1.
a)
Graph each of the lines in the system of equations shown below and
estimate the point of intersection.
4x + y + 1 = 0
3x - 2y = -8
b)
c)
2.
3.
4.
Solve the system using substitution (use fractions, not decimals!)
Explain why there might be a difference between the two answers.
Solve the following systems using substitution.
a)
x + 2y = 1
b)
3x - 4y = 32
x - 3y = 11
5x - y = 25
Solve the following systems using elimination.
a)
5x - 2y = 10
b)
3a - b = 4
x + 2y = 2
a - 2b = 3
c) 2x + y = -8
10x - 3y - 16 = 0
c)
4x + 3y = 10
5x - 7y = -52
Solve the following systems using an algebraic method of your choice.
a)
5v + u = -17
b)
3x + y = 2
3u - 4v = 6
6x - 3y + 16 = 0
c)
5x - 2y = -9
3x + 7y = 11
d)
4c - 5d = -2
8c + 10d = 8
5. White vinegar is a solution of acetic acid in water. There are two strengths of white
vinegar – a 7% solution and a 12% solution. How many millilitres of each solution must
be mixed to make 50 mL of a 10% vinegar solution?
6. A plane took 6 hours to fly 6300 km from Yukon to Halifax with a tail wind. The return
trip, with a head wind, took 7 hours. Find the speed of the plane in still air and the wind
speed.
7. Cindy and the Interact Club decided to hold a car wash to raise money. They washed
cars for $5 each and vans for $7 each. They washed 45 vehicles and earned $275. How
many of each type of vehicle did they wash?
8. Sarah took 7 hours to drive 550 km from Windsor to Peterborough. For part of the
trip, she drove at 85 km/h and for the rest of the trip, drove at 70 km/h. How far did she
drive at each speed?
9. Grace invested $6000, part at 5% per year and the rest at 8% per year. After one
year, the total interest from these investments was $426. How much money did she
invest at each rate?
-------------------------------------------------------------------------------------------------Answers :
1b) (-10/11 ,29/11); 2a) (5, -2); b) (4, -5); c) (-½, -7); 3a) (2,0); b) (1,-1);
c) (-2,6); 4a) (-2,-3); b) (- , 4); c) (-1,2); d) (¼, 3/5) 5) 20ml of 7% and 30ml of 12%; 6) plane
speed is 975 km/h, wind speed is 75 km/h; 7) 20 cars & 25 vans; 8) 340km at 85km/h and
210km at 70km/h; 9) $1800 at 5% and $4200 at 8%