Test 3 – Updated version A
MAT 114
Name __________________________
1)
Classify the system as consistent or inconsistent, dependent or independent
2x – 5y = −4
10x – 25y = −20
2)
Classify the system as consistent or inconsistent, dependent or independent
x + y = −5
x–y =3
3)
Solve system of equations by graphing (use the graph provided below)
3x + y = – 9
x + y = –1
y
x
4)
Solve system of equations using either substitution or elimination method
y = 2x +3
3x + y = −17
5)
Solve system of equations using either substitution or elimination method
x − 4y = −5
2x − 4y= −6
6)
Solve system of equations using either substitution or elimination method
x + 5y = −2
−3x + 6y = 6
7)
Solve system of equations using either substitution or elimination method
− 4x − 2y = −6
− 12x − 6y= 18
8) Solve system of 3 equations
x+y+z=2
x – y + 2z = –2
3x + y + z = –4
9) Solve system of inequalities by graphing (use the graph provided below)
x + 2y ≤ 2
y ≥ –x
y
x
Part III: Create system of equations for 3 problems, but you only have to solve 2 of them.
10) How many liters of a 10% alcohol solution and how many liters of a 30% alcohol solution must be
mixed together to get 320 liters of a 20% alcohol solution?
11) Mardi received an inheritance of $70,000. She invested part of it at 9% and part at 12%. Her total
annual income from the investment was $7200. Find the amount invested at 9% and 12%.
12) The speed of a stream is 5mph. If a boat travels 48 miles downstream in the same time that it takes to
travel 24 miles upstream, what is the speed of the boat in still water?
13) A cabin cruiser travels 20 miles in the same time that a power boat travels 40 miles. The cruiser
travels 5 mph slower than the power boat. Find the speed of each boat.