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Systems of Equations
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4. Use elimination to find the solution to the system
of equations.
1.
-3x - 4y = -24
-2x + 4y = 4
A.
Find the solution to the system of equations shown
above by graphing.
A. x = 5, y = 3
B.
B. x = 4, y = 4
C. x = 3, y = 4
D. x = 4, y = 3
C.
D.
2.
5. Find the solution to the system of equations given
below using elimination by addition.
Using the two equations above, solve for y.
A.
B.
C.
A.
B.
D.
C.
3.
Describe the solution to the system of equations
below.
The system has infinitely many solutions of
the form y = 5x - 8, where x is any real
A.
number.
B.
C.
D.
The system has the unique solution (-6, -38).
The system has the unique solution (4, 12).
The system has no solution.
D.
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6.
Systems of Equations
9. Describe the solution to the system of equations
graphed below.
2x + y = -4
6x + 3y = -12
A.
B.
C.
D.
7.
A. The system has no solution.
B. The system has the unique solution (2, 2).
A.
C. The system has the unique solution (3, 12).
B.
The system has infinitely many solutions of
D. the form y = -2x - 4 where x is any real
number.
C.
D.
10. Use elimination to find the solution to the
system of equations.
8. Find the solution to the system of equations given
below using elimination by addition.
3x + 15y = 30
x + 3y = 6
A.
B.
C.
D.
A.
x = -12, y = 6
B.
x = 24, y = -6
C.
x = 12, y = -2
D.
x = 0, y = 2
Name _____________________________
Systems of Equations
Answers
1. D
2. A
3. D
4. D
5. D
6. D
7. C
8. D
9. D
10. D
Now, substitute x into the first equation.
Explanations
1. Graph each equation on the coordinate plane. The
point of intersection of the two graphs gives the
solution to the system of equations.
3. One way to solve a system of equations is to
graph the equations, and find the point of
intersection. Start by placing both equations in
slope-intercept form.
Notice that both equations have the same slope but
different y-intercepts. The two lines are parallel and
will never intersect. Thus, the system has no
solution.
4. Use elimination by addition to solve the system
of equations.
The two lines intersect at (4, 3). So, x = 4 and y = 3
is the solution.
2.
First, solve the second equation for x.
Start by eliminating the y-terms, and then solve for
x.
Name _____________________________
Next, substitute x = 3 into one of the original
equations and solve for y.
Systems of Equations
7.
8. Use elimination by addition to solve the system
of equations.
3x + 15y = 30
x + 3y = 6
Therefore, the solution to the system of equations is
x = 3, y = 1.
5. Use elimination by addition to solve the system
of equations.
Start by eliminating the x term. To do this, multiply
the second equation by -3, and then add the two
equations together.
3x + 15y = 30
-3x - 9y = -18
Start by eliminating the y term. To do this, multiply
the first equation by -5, and then add the two
equations together.
Next, substitute x = -9 into the first equation, and
solve for y.
6y = 12
y= 2
Next, substitute y = 2 into the original second
equation, and solve for x.
x + 3y = 6
x + 3(2) = 6
x+6=6
x=6-6
x=0
Therefore, the solution to the system of equations is
x = 0, y = 2.
9. Notice that there is only one line graphed and
when solved for y, both equations have the same
slope and the same y-intercept. The two equations
graph the same line that will intersect at infinitely
many points.
Therefore, the solution to the system of equations is
.
6.
Thus, the system has infinitely many solutions of
the form y = -2x - 4 where x is any real number.
10. Use elimination by addition to solve the system
of equations.
Start by eliminating the y-terms, and then solve for
x.
Name _____________________________
Next, substitute x = 3 into one of the original
equations and solve for y.
Therefore, the solution to the system of equations is
x = 3, y = -6.
Systems of Equations