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Chapter 7 Test
Review
Algebra 1
Name________________
Date_________________
In order for a point (x, y) to be a solution, we need to plug each variable in and check.
If the statement is true, then it _____ a solution. If false, then it is ______ a solution.
Decide whether each ordered pair is a solution of the system of linear equations.
x  3y  6
 4x  y  8
 2x  3y  6
1.
(-6, -4)
2.
(-1, 4)
3.
(0, -2)
2 x  y  8
5 x  3 y  3
3x  4 y  10
Use the graph to estimate the solution of the linear system. Then, check your solution.
 x  y  8
3 x  y  6
4.
5.
 x  2 y  3
x y 4
Solution__________
Solution__________
Check Your Solution Here:
6.
4 x  2 y  12
2x  2 y  8
Solution__________
Check Your Solution Here:
Check Your Solution Here:
2x  y  3
x  2y  4
7.
Solution__________
Check Your Solution Here:
When graphing a line, it needs to be in ________________________________:_____________
First I graph the y-intercept by putting a dot on the _____________________________
Then, I move from that dot and graph the slope using _____________ over _____________
Graph the following linear systems. Then find the solution and check it.
8.
x6
y  2
9.
y  x2
y  x  4
Solution:____________
Solution:____________
Check Your Solution Here:
Check Your Solution Here:
y  2 x  4
10.
1
y   x 1
2
11.
Solution:____________
Solution:____________
Check Your Solution Here:
Check Your Solution Here:
3x  y  6
 x  y  2
When using the SUBSTITUTION method, the first thing I do is get one of the variables alone
Then, we plug that new expression into the other equation and solve
Be sure to solve for __________________ variables!!
Use the substitution method to solve the linear system.
y  x2
2x  y  3
12.
13.
2x  y  8
y7
Final Answer:______________________
14.
3 x  y  2
y  2x  3
Final Answer:______________________
15.
Final Answer:______________________
16.
3x  y  9
2x  y  6
Final Answer:______________________
x  y  3
3x  y  3
Final Answer:______________________
17.
x  2y  0
3x  y  0
Final Answer:______________________
When using the ELIMINATION method, the first thing I do is line up all the like terms vertically
Then, I multiply one, or both, of the equations by some numbers to get one of the variables to have
the __________________ number and ____________________ signs.
Next, I add straight down and solve. Be sure to solve for ______________ variables and check!
Solve the following systems of equations using the Elimination method.
x y 5
3x  y  6
18.
19.
x y 7
 3x  4 y  9
Final Answer:______________________
20.
2x  y  1
2 x  5 y  5
Final Answer:______________________
21.
Final Answer:______________________
22.
2 x  5 y  22
4x  3 y  8
Final Answer:______________________
x  3 y  3
x  4 y  11
Final Answer:______________________
23.
 4x  y  3
6 x  y  7
Final Answer:______________________
24.
x  2 y  3
x  4 y  15
25.
Final Answer:______________________
3x  8 y  4
5 x  4 y  28
Final Answer:______________________
When solving a system of equations graphically, if the lines are ______________________, the
system has _________ solution. If that happens, then algebraically, the variables will
________________________ and you will be left with a ________________ statement
When solving a system of equations graphically, if the lines are _________________, the
system has _______________ solutions. If that happens, then algebraically, the variables will
________________________ and you will be left with a ________________ statement
Solve the following systems.
3x  5 y  7
26.
 3x  5 y  8
27.
Final Answer:______________________
28.
3x  4 y  8
9 x  12 y  24
Final Answer:______________________
 x  3 y  5
2 x  6 y  10
Final Answer:______________________
29.
2x  3y  1
4x  6 y  3
Final Answer:______________________
Solving a System of Linear Inequalities
1.
Write _____________ inequalities in _______________________________ : ______________
2.
__________________ both inequalities in the same pictures
Remember, plot the __________________ first, then use the ______________ for rise over run
3.
_______________________ accordingly and darken the ___________________ area
4.
Any point in the ____________________ region is a solution to the system of linear inequalities!
Solve the following linear systems by graphing. Once you have graphed and shaded, identify
two solutions.
30.
y3
x  2
31.
Two Points:____________________
32.
1
x3
2
y  x 1
y
Two Points:____________________
y  x3
y  x 1
Two Points:____________________
33.
y  x  4
4
y   x2
3
Two Points:____________________