Name: ____________________________________________
Chapter 6 Test Review
Solve the following by graphing:
1.) y = -4x + 10 and y = 2x - 8
2.) 6x+ 2y = 12 and y = -3x + 6
3.) Write the equation of a line that would have no solution when it is in a system with the line
y = 3x + 7.
4.) Without graphing determine how many solutions the following system has. Explain your
reasoning.
Y = 6x + 2 and 6x +y = 12
5.) Solve the following by substitution.
a.) y = -5x and -3x + y =16
b.) y = 2x + 1 and 6x + 2y = – 38
6.) Solve the following by substitution.
a.) -2x+ 6y = 12 and 2x + y = 16
b.) 3x + 5y = 13 and -4x + y = – 2
7.) Solve the following by elimination.
a.) 1y + 4x = 10
1y – 2x = – 8
c.) 3x + 5y = 11
2x + 4y = 8
b.) x – 4y = – 8
-2x +8y = – 32
Solve the following by writing a system of linear equations and then solving the system by one of
the three methods we have studied in this chapter. Be sure to define your variables.
8.) A silly little mouse is trying to figure out how many cows and how many chickens there are
on his farm. He knows that there are 19 animals and he counted 54 legs. How many cows and
how many chickens are there?
9.) Tyrone is selling ice cream cones at the fair. He is able to sell each one for $4. The cost of the
actual ice cream is $2.50 and the cost of the booth is $84. How many ice cream cones does he
have to sell to “break even”?
10.) A man is kayaking up river an then back down. If he is moving at a rate of 3 mph compared
to the shore when moving up river, and 11 mph when moving down river then how fast is he
actually paddling, and how fast is the river moving?
11.) Glen is quite the salesman. He is selling candy bars and so is Sally. He is so confident that he
is a better salesman that he stated that he will give her $50 and will sell his candy for more
money and he will still make more than her. If he is selling his candy for $3.50 a piece and she is
selling hers for $2.25 then how many candies need to be sold before they both have the same
amount of money?
Solve the following system of linear inequalities by graphing.
3
12.) y   x  8 and y  x  3
4
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13.) y 
2
x  4 and 2x – 3y < – 6
3
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14.) What is the system of linear inequalities that is represented by the following graph?