Resources
Testimonials
Plans
Sign in
Sign up
Resources
Testimonials
Plans
Home
Math Problems
Algebra 2
Determine the number of solutions to a system of equations in three variables
Does the following equation have one solution, no solutions, or infinitely many solutior
\newline
4
−
3
x
=
−
3
(
x
−
5
)
−
7
4-3 x=-3(x-5)-7
4
−
3
x
=
−
3
(
x
−
5
)
−
7
\newline
1
1
1
\newline
2
2
2
\newline
□
\square
□
\newline
□
\square
□
3
3
3
\newline
Tax Day
\newline
Today
\newline
United States
\newline
邓
0
0
0
\newline
1
/
21
1 / 21
1/21
\newline
8
−
8-
8
−
\newline
68289
68289
68289
\newline
oes the following equation have one solution, no solutions, or infinitely many solutior
\newline
This cannot be
\newline
One
\newline
None determined
\newline
leah
Get tutor help
How many solutions does the system of equations below have?
\newline
2
x
+
3
y
+
2
z
=
−
19
2x + 3y + 2z = -19
2
x
+
3
y
+
2
z
=
−
19
\newline
−
2
x
−
2
y
+
2
z
=
5
-2x - 2y + 2z = 5
−
2
x
−
2
y
+
2
z
=
5
\newline
−
x
−
2
y
−
3
z
=
−
15
-x - 2y - 3z = -15
−
x
−
2
y
−
3
z
=
−
15
\newline
Choices:
\newline
(A)no solution
\newline
(B)one solution
\newline
(C)infinitely many solutions
Get tutor help
How many solutions does the system of equations below have?
\newline
−
2
x
−
y
−
3
z
=
−
13
-2x - y - 3z = -13
−
2
x
−
y
−
3
z
=
−
13
\newline
−
x
−
y
+
z
=
−
3
-x - y + z = -3
−
x
−
y
+
z
=
−
3
\newline
3
x
+
2
y
+
2
z
=
16
3x + 2y + 2z = 16
3
x
+
2
y
+
2
z
=
16
\newline
Choices:
\newline
(A)no solution
\newline
(B)one solution
\newline
(C)infinitely many solutions
Get tutor help
How many solutions does the system of equations below have?
\newline
−
2
x
+
3
y
−
3
z
=
−
13
-2x + 3y - 3z = -13
−
2
x
+
3
y
−
3
z
=
−
13
\newline
−
2
x
+
2
y
−
3
z
=
−
18
-2x + 2y - 3z = -18
−
2
x
+
2
y
−
3
z
=
−
18
\newline
2
x
+
y
−
2
z
=
3
2x + y - 2z = 3
2
x
+
y
−
2
z
=
3
\newline
Choices:
\newline
(A)no solution
\newline
(B)one solution
\newline
(C)infinitely many solutions
Get tutor help
How many solutions does the system of equations below have?
\newline
−
2
x
−
2
y
−
z
=
3
-2x - 2y - z = 3
−
2
x
−
2
y
−
z
=
3
\newline
x
−
3
y
+
z
=
17
x - 3y + z = 17
x
−
3
y
+
z
=
17
\newline
3
x
+
2
y
−
z
=
−
13
3x + 2y - z = -13
3
x
+
2
y
−
z
=
−
13
\newline
Choices:
\newline
(A)no solution
\newline
(B)one solution
\newline
(C)infinitely many solutions
Get tutor help
How many solutions does the system of equations below have?
\newline
x
−
2
y
−
z
=
3
x - 2y - z = 3
x
−
2
y
−
z
=
3
\newline
−
2
x
+
3
y
−
3
z
=
0
-2x + 3y - 3z = 0
−
2
x
+
3
y
−
3
z
=
0
\newline
2
x
+
2
y
−
3
z
=
1
2x + 2y - 3z = 1
2
x
+
2
y
−
3
z
=
1
\newline
Choices:
\newline
(A)no solution
\newline
(B)one solution
\newline
(C)infinitely many solutions
Get tutor help
How many solutions does the system of equations below have?
\newline
−
3
x
+
y
−
3
z
=
4
-3x + y - 3z = 4
−
3
x
+
y
−
3
z
=
4
\newline
x
−
y
−
z
=
16
x - y - z = 16
x
−
y
−
z
=
16
\newline
3
x
−
y
+
3
z
=
−
4
3x - y + 3z = -4
3
x
−
y
+
3
z
=
−
4
\newline
Choices:
\newline
(A)no solution
\newline
(B)one solution
\newline
(C)infinitely many solutions
Get tutor help
How many solutions does the system of equations below have?
\newline
3
x
−
3
y
+
3
z
=
3
3x - 3y + 3z = 3
3
x
−
3
y
+
3
z
=
3
\newline
−
x
+
y
−
z
=
−
1
-x + y - z = -1
−
x
+
y
−
z
=
−
1
\newline
−
2
x
+
2
y
−
2
z
=
−
2
-2x + 2y - 2z = -2
−
2
x
+
2
y
−
2
z
=
−
2
\newline
Choices:
\newline
(A)no solution
\newline
(B)one solution
\newline
(C)infinitely many solutions
Get tutor help
How many solutions does the system of equations below have?
\newline
2
x
−
y
−
z
=
−
13
2x - y - z = -13
2
x
−
y
−
z
=
−
13
\newline
3
x
−
2
y
−
z
=
−
20
3x - 2y - z = -20
3
x
−
2
y
−
z
=
−
20
\newline
−
3
x
+
y
+
2
z
=
19
-3x + y + 2z = 19
−
3
x
+
y
+
2
z
=
19
\newline
Choices:
\newline
(A)no solution
\newline
(B)one solution
\newline
(C)infinitely many solutions
Get tutor help
How many solutions does the system of equations below have?
\newline
−
10
x
+
3
y
=
−
8
20
x
−
6
y
−
16
=
0
\begin{array}{l} -10 x+3 y=-8 \\ 20 x-6 y-16=0 \end{array}
−
10
x
+
3
y
=
−
8
20
x
−
6
y
−
16
=
0
\newline
(A) no solution
\newline
(B) one solution
\newline
(C) infinitely many solutions
Get tutor help
Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.
\newline
2
x
+
5
y
=
−
7
−
2
x
−
2
y
=
6
\begin{aligned} 2 x+5 y & =-7 \\ -2 x-2 y & =6 \end{aligned}
2
x
+
5
y
−
2
x
−
2
y
=
−
7
=
6
\newline
One Solution
\newline
No Solutions
\newline
Infinitely Many Solutions
Get tutor help
Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.
\newline
−
5
x
+
3
y
=
2
5
x
−
3
y
=
−
5
\begin{aligned} -5 x+3 y & =2 \\ 5 x-3 y & =-5 \end{aligned}
−
5
x
+
3
y
5
x
−
3
y
=
2
=
−
5
\newline
No Solutions
\newline
One Solution
\newline
Infinitely Many Solutions
Get tutor help
Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.
\newline
x
+
2
y
=
−
4
4
x
+
8
y
=
−
16
\begin{array}{c} x+2 y=-4 \\ 4 x+8 y=-16 \end{array}
x
+
2
y
=
−
4
4
x
+
8
y
=
−
16
\newline
No Solutions
\newline
One Solution
\newline
Infinitely Many Solutions
Get tutor help
Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.
\newline
−
x
+
2
y
=
−
4
−
2
x
+
7
y
=
−
6
\begin{array}{r} -x+2 y=-4 \\ -2 x+7 y=-6 \end{array}
−
x
+
2
y
=
−
4
−
2
x
+
7
y
=
−
6
\newline
Infinitely Many Solutions
\newline
One Solution
\newline
No Solutions
Get tutor help
Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.
\newline
x
+
3
y
=
2
2
x
+
6
y
=
4
\begin{aligned} x+3 y & =2 \\ 2 x+6 y & =4 \end{aligned}
x
+
3
y
2
x
+
6
y
=
2
=
4
\newline
One Solution
\newline
Infinitely Many Solutions
\newline
No Solutions
Get tutor help
Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.
\newline
−
4
x
+
5
y
=
3
4
x
−
5
y
=
−
6
\begin{aligned} -4 x+5 y & =3 \\ 4 x-5 y & =-6 \end{aligned}
−
4
x
+
5
y
4
x
−
5
y
=
3
=
−
6
\newline
No Solutions
\newline
One Solution
\newline
Infinitely Many Solutions
Get tutor help
Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.
\newline
x
+
4
y
=
−
5
4
x
+
16
y
=
−
20
\begin{aligned} x+4 y & =-5 \\ 4 x+16 y & =-20 \end{aligned}
x
+
4
y
4
x
+
16
y
=
−
5
=
−
20
\newline
Infinitely Many Solutions
\newline
One Solution
\newline
No Solutions
Get tutor help
Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.
\newline
3
x
+
y
=
4
12
x
+
4
y
=
16
\begin{array}{c} 3 x+y=4 \\ 12 x+4 y=16 \end{array}
3
x
+
y
=
4
12
x
+
4
y
=
16
\newline
Infinitely Many Solutions
\newline
One Solution
\newline
No Solutions
Get tutor help
Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.
\newline
x
+
y
=
−
7
−
2
x
−
2
y
=
14
\begin{aligned} x+y & =-7 \\ -2 x-2 y & =14 \end{aligned}
x
+
y
−
2
x
−
2
y
=
−
7
=
14
\newline
Infinitely Many Solutions
\newline
No Solutions
\newline
One Solution
Get tutor help
Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.
\newline
−
2
x
+
3
y
=
−
1
2
x
−
6
y
=
4
\begin{aligned} -2 x+3 y & =-1 \\ 2 x-6 y & =4 \end{aligned}
−
2
x
+
3
y
2
x
−
6
y
=
−
1
=
4
\newline
No Solutions
\newline
Infinitely Many Solutions
\newline
One Solution
Get tutor help
Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.
\newline
−
x
+
2
y
=
5
2
x
−
4
y
=
−
8
\begin{array}{l} -x+2 y=5 \\ 2 x-4 y=-8 \end{array}
−
x
+
2
y
=
5
2
x
−
4
y
=
−
8
\newline
Infinitely Many Solutions
\newline
No Solutions
\newline
One Solution
Get tutor help
Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.
\newline
−
x
+
2
y
=
−
5
−
4
x
+
8
y
=
−
23
\begin{aligned} -x+2 y & =-5 \\ -4 x+8 y & =-23 \end{aligned}
−
x
+
2
y
−
4
x
+
8
y
=
−
5
=
−
23
\newline
Infinitely Many Solutions
\newline
One Solution
\newline
No Solutions
Get tutor help
How many solutions does the system of equations below have?
\newline
x
+
3
y
+
2
z
=
5
x + 3y + 2z = 5
x
+
3
y
+
2
z
=
5
\newline
x
+
2
y
−
2
z
=
16
x + 2y - 2z = 16
x
+
2
y
−
2
z
=
16
\newline
−
2
x
+
2
y
−
z
=
−
11
-2x + 2y - z = -11
−
2
x
+
2
y
−
z
=
−
11
\newline
Choices:
\newline
[A]no solution
\text{[A]no solution}
[A]no solution
\newline
[B]one solution
\text{[B]one solution}
[B]one solution
\newline
[C]infinitely many solutions
\text{[C]infinitely many solutions}
[C]infinitely many solutions
Get tutor help