System of Equations Review
Name:
1.
Date:
Solve the following system of equations for x:
6.
x+y=6
x y=2
2.
2x + 3y = 5
4x 3y = 1
Solve the following system of equations
algebraically and check:
7.
x 4y = 16
y=1 x
3.
Solve the following system of equations for x:
8.
Solve algebraically and check:
4x + 3y = 12
2x + y = 16
Solve the following system of equations
algebraically and check:
9.
Solve graphically and check:
2x + y = 5
x 2y = 10
3x + 2y = 6
5x 3y = 28
5.
Solve the following system of equations graphically
and check:
3x + y = 3
y = 2x 7
3x + y = 9
2x y = 6
4.
Solve the following systems of equations for x:
10.
Solve the following system of equations for x:
3x + 3y = 21
6x 3y = 6
Solve the following system of equations graphically
and check:
2x + y = 1
x + 2y = 4
page 1
11.
Solve the following system of equations graphically
and check:
15.
Which ordered pair is the solution to this system
of equations?
y = 3x 7
2x + 3y = 12
12.
2x y = 10
x+y=2
16.
A.
(1; 5)
B.
B.
C.
(2; 4)
D. ( 4; 2)
(4; 2)
C.
( 1; 3)
D. ( 4; 0)
What is the solution for x in the following system
of equations?
y = 2x 3
y= x+1
(0; 2)
A.
17.
Solve the following system of equations
algebraically and check:
4x + 3y = 25
5x + 2y = 33
14.
(4; 2)
Which ordered pair is the solution to this system
of equations?
y=x+4
x+y=2
13.
A.
Solve the following system of equations graphically
and check:
18.
y = 2x + 3
x 2y = 6
2
3
B.
2
C.
4
3
D. 4
When solved graphically, which system of
equations will have exactly one point of
intersection?
A.
y = x 20
y = x + 17
B.
y = 0:5x + 30
y = 0:5x 30
C.
y = 35 x + 12
y = 0:6x 19
D.
y = x + 15
y = x + 25
On the same set of coordinate axes, graph the
following system of inequalities and label the
solution set S:
x+y<3
y 2x
page 2
System of Equations Review
19.
Which ordered pair is in the solution set of the
system of inequalities shown in the graph?
22.
The accompanying diagram represents the graphs
of the inequalities y 3 and x < 2.
Which ordered pair names a point in the solution
set of this system of inequalities?
A.
(0; 0)
B.
(1; 5)
C.
( 3; 3)
D. (3; 3)
A.
(3; 5)
B.
(3; 5)
C.
( 3; 5)
D. ( 3; 5)
20.
On the same set of coordinate axes, graph the
following system of inequalities. Label the
solution set S.
y
x
21.
2x + 4
y<1
23.
Which point is in the solution set of the system of
inequalities shown in the accompanying graph?
Which ordered pair is in the solution set of the
system of inequalities shown in the accompanying
graph?
A.
(2; 5)
B.
(2; 2)
C.
(4; 3)
D. ( 4; 3)
page 3
A.
(0; 4)
B.
(2; 4)
C.
( 4; 1)
D. (4; 1)
System of Equations Review
24.
Which ordered pair is in the solution set to the
system of inequalities shown in the accompanying
graph?
25.
Graph the following systems of inequalities on the
accompanying set of axes and label the solution
set S:
y>x
y+x
4
2
[Only a graphic solution can receive full credit.]
A.
(0; 0)
B.
(0; 1)
C.
(1; 5)
D. (3; 2)
26.
Which ordered pair is in the solution set of the
following system of inequalities?
y < 12 x + 4
y
x+1
page 4
A.
( 5; 3)
B.
(0; 4)
C.
(3; 5)
D. (4; 0)
System of Equations Review
27.
Graph the following system of inequalities on the
set of axes shown below and label the solution
set S.
y >
y
28.
On the set of axes below, solve the following
system of inequalities graphically. Label the
solution set S.
x+2
2x + 3y < 3
y 4x 2
2x + 5
29.
The graphs of the equations x2 + y2 = 4 and y = 2
are drawn on the same set of axes. What is the
total number of points common to both graphs?
A.
30.
1
B.
2
C.
3
D. 4
Solve the following system of equations
algebraically and check.
y = x2 + 3x + 4
y x=7
page 5
System of Equations Review
31.
Solve the following system of equations
algebraically and check:
34.
y = 3x2 8x + 5
x+y=3
Solve the following system of equations
algebraically or graphically for x and y:
y = x2 + 2x
y = 3x + 5
1
For an algebraic solution, show your work here.
For a graphic solution, show your work here.
32.
33.
Which is a point of intersection of the graphs of
y = 4 x and y = x2 x ?
A.
(3; 1)
B.
( 1; 5)
C.
( 2; 6)
D. (4; 0)
Solve the following system of equations and check:
y = x2
y = 2x
4x + 3
2
page 6
System of Equations Review
Solve the following system of equations:
36.
y = x2 + 4x + 1
Solve the following system of equations
algebraically or graphically for x and y:
y = x2 + 4x + 6
y = 2x + 6
y = 5x + 3
…
[The use of the grid below is optional.]
y
x

…

35.
page 7
System of Equations Review
37.
Which ordered pair is a solution of the system of
equations shown in the graph below?
38.
On the set of axes below, solve the following
system of equations graphically for all values of x
and y.
y = x2 4x + 12
y = 2x + 4
A.
( 3; 1)
B.
( 3; 5)
C.
(0; 1)
D. (0; 4)
page 8
System of Equations Review
39.
Which graph can be used to nd the solution of the following system of equations?
y = x2 + 2x + 3
2y 2x = 10
A.
B.
C.
D.
page 9
System of Equations Review
40.
Which graph could be used to nd the solution of the system of equations y = 2x + 6 and y = x2 + 4x + 3?
A.
B.
C.
D.
page 10
System of Equations Review
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System of Equations Review
05/01/2015
1.
Answer:
4
20.
Answer:
[graph]
2.
Answer:
x = 4, y = 3
21.
Answer:
B
3.
Answer:
3
22.
Answer:
C
4.
Answer:
( 2; 6)
23.
Answer:
C
5.
Answer:
3
24.
Answer:
D
6.
Answer:
1
25.
Answer:
[task]
7.
Answer:
[graph]
26.
Answer:
D
8.
Answer:
x = 6, y = 4
27.
Answer:
9.
Answer:
x = 4, y = 3
28.
Answer:
Both inequalities are graphed and shaded
correctly, and at least one is labeled, and
the solution set is labeled S.
Both inequalities are graphed and shaded
correctly, and at least one is labeled. The
solution set is labeled S.
10.
Answer:
x = 2, y = 3
11.
Answer:
x = 3, y = 2
12.
Answer:
29.
Answer:
A
C
13.
Answer:
30.
Answer:
(1; 8) and ( 3; 4)
x = 7, y = 1
14.
Answer:
31.
Answer:
(2; 1) and ( 31 ;
x = 0, y = 3
15.
Answer:
32.
Answer:
C
A
16.
Answer:
33.
Answer:
(1; 0) and (5; 8)
B
17.
Answer:
34.
Answer:
(3; 14) and ( 2; 1)
A
18.
Answer:
35.
Answer:
( 1; 2) and (2; 13)
[graph]
19.
Answer:
36.
Answer:
( 2; 2) and (0; 6)
A
37.
Answer:
B
8
3)
Teacher's Key
38.
Answer:
(2; 0) and ( 4; 12)
39.
Answer:
A
40.
Answer:
D
Page 2