Resources
Testimonials
Plans
Sign in
Sign up
Resources
Testimonials
Plans
Home
Math Problems
Algebra 2
Find the number of solutions to a system of equations
x
−
y
=
y
−
4
+
2
(
4.5
−
2
x
)
4
(
x
+
2
y
)
=
−
p
+
7
y
\begin{aligned} x-y & =y-4+2(4.5-2 x) \\ 4(x+2 y) & =-p+7 y \end{aligned}
x
−
y
4
(
x
+
2
y
)
=
y
−
4
+
2
(
4.5
−
2
x
)
=
−
p
+
7
y
\newline
In the system of equations,
p
p
p
is a constant. For which value of
p
p
p
is there exactly one solution
(
x
,
y
)
(x, y)
(
x
,
y
)
where
x
=
−
1
x=-1
x
=
−
1
?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
5
-5
−
5
\newline
(B)
9
9
9
\newline
(C) Any real number
\newline
(D) None of the above
Get tutor help
x
+
6
y
=
r
−
2
x
x+6 y=r-2 x
x
+
6
y
=
r
−
2
x
\newline
2
(
x
+
4
)
+
2
y
=
11
+
1
2
(
16
+
2
x
)
2(x+4)+2 y=11+\frac{1}{2}(16+2 x)
2
(
x
+
4
)
+
2
y
=
11
+
2
1
(
16
+
2
x
)
\newline
In the system of equations,
r
r
r
is a constant. For what value of
r
r
r
does the system of linear equations have infinitely many solutions?
Get tutor help
6
(
y
−
4
)
=
x
−
3
6(y-4)=x-3
6
(
y
−
4
)
=
x
−
3
\newline
y
=
C
y=C
y
=
C
\newline
In the system of equations,
C
C
C
is a constant. For which value of
C
C
C
is
(
x
,
y
)
=
(
−
3
,
3
)
(x, y)=(-3,3)
(
x
,
y
)
=
(
−
3
,
3
)
a solution?
\newline
Choose
1
1
1
answer:
\newline
(A)
3
3
3
\newline
(B)
21
21
21
\newline
(C) All real numbers
\newline
(D) None of the above
Get tutor help
How many solutions does the system have?
\newline
{
y
=
−
3
x
+
9
3
y
=
−
9
x
+
9
\left\{\begin{array}{l} y=-3 x+9 \\ 3 y=-9 x+9 \end{array}\right.
{
y
=
−
3
x
+
9
3
y
=
−
9
x
+
9
\newline
Choose
1
1
1
answer:
\newline
(A) Exactly one solution
\newline
(B) No solutions
\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
x
+
3
y
=
1
2
x
+
6
y
=
4
\begin{array}{r} x+3 y=1 \\ 2 x+6 y=4 \end{array}
x
+
3
y
=
1
2
x
+
6
y
=
4
\newline
Infinitely Many Solutions
\newline
No Solutions
\newline
One Solution
Get tutor help
How many solutions does the system have?
\newline
{
3
y
=
−
6
x
+
9
y
=
−
6
x
+
9
\begin{cases}3y=-6x+9\\y=-6x+9\end{cases}
{
3
y
=
−
6
x
+
9
y
=
−
6
x
+
9
\newline
Choose
1
1
1
answer:
\newline
(A) Exactly one solution
\newline
(B) No solutions
\newline
(C) Infinitely many solutions
Get tutor help
How many solutions does the system have?
\newline
{
6
x
−
y
=
−
1
6
x
+
y
=
−
1
\left\{\begin{array}{l} 6 x-y=-1 \\ 6 x+y=-1 \end{array}\right.
{
6
x
−
y
=
−
1
6
x
+
y
=
−
1
\newline
Choose
1
1
1
answer:
\newline
(A) Exactly one solution
\newline
(B) No solutions
\newline
(C) Infinitely many solutions
Get tutor help
How many solutions does the system have?
\newline
{
y
=
−
5
x
+
1
y
=
1
−
5
x
\left\{\begin{array}{l} y=-5 x+1 \\ y=1-5 x \end{array}\right.
{
y
=
−
5
x
+
1
y
=
1
−
5
x
\newline
Choose
1
1
1
answer:
\newline
(A) Exactly one solution
\newline
(B) No solutions
\newline
(C) Infinitely many solutions
Get tutor help
How many solutions does the system have?
\newline
{
y
=
−
3
x
+
9
3
y
=
−
9
x
+
9
\left\{\begin{array}{l} y=-3 x+9 \\ 3 y=-9 x+9 \end{array}\right.
{
y
=
−
3
x
+
9
3
y
=
−
9
x
+
9
\newline
Choose
1
1
1
answer:
\newline
(A) Exactly one solution
\newline
(B) No solutions
\newline
(C) Infinitely many solutions
Get tutor help
How many solutions does the system have?
\newline
{
y
=
9
x
−
5
y
=
9
x
+
6
\left\{\begin{array}{l} y=9 x-5 \\ y=9 x+6 \end{array}\right.
{
y
=
9
x
−
5
y
=
9
x
+
6
\newline
Choose
1
1
1
answer:
\newline
(A) Exactly one solution
\newline
(B) No solutions
\newline
(C) Infinitely many solutions
Get tutor help
How many solutions does the system have?
\newline
{
20
x
−
5
y
=
5
4
x
−
y
=
1
\left\{\begin{array}{l} 20 x-5 y=5 \\ 4 x-y=1 \end{array}\right.
{
20
x
−
5
y
=
5
4
x
−
y
=
1
\newline
Choose
1
1
1
answer:
\newline
(A) Exactly one solution
\newline
(B) No solutions
\newline
(C) Infinitely many solutions
Get tutor help
How many solutions does the system have?
\newline
{
3
y
=
−
6
x
+
9
y
=
−
6
x
+
9
\left\{\begin{array}{l} 3 y=-6 x+9 \\ y=-6 x+9 \end{array}\right.
{
3
y
=
−
6
x
+
9
y
=
−
6
x
+
9
\newline
Choose
1
1
1
answer:
\newline
(A) Exactly one solution
\newline
(B) No solutions
\newline
(C) Infinitely many solutions
Get tutor help
How many solutions does the system have?
\newline
{
y
=
−
2
x
−
4
y
=
3
x
+
3
\left\{\begin{array}{l} y=-2 x-4 \\ y=3 x+3 \end{array}\right.
{
y
=
−
2
x
−
4
y
=
3
x
+
3
\newline
Choose
1
1
1
answer:
\newline
(A) Exactly one solution
\newline
(B) No solutions
\newline
(C) Infinitely many solutions
Get tutor help
How many solutions does the system have?
\newline
{
5
y
=
15
x
−
40
y
=
3
x
−
8
\left\{\begin{array}{l} 5 y=15 x-40 \\ y=3 x-8 \end{array}\right.
{
5
y
=
15
x
−
40
y
=
3
x
−
8
\newline
Choose
1
1
1
answer:
\newline
(A) Exactly one solution
\newline
(B) No solutions
\newline
(C) Infinitely many solutions
Get tutor help
How many solutions does the system have?
\newline
{
y
=
−
2
x
+
4
7
y
=
−
14
x
+
28
\left\{\begin{array}{l} y=-2 x+4 \\ 7 y=-14 x+28 \end{array}\right.
{
y
=
−
2
x
+
4
7
y
=
−
14
x
+
28
\newline
Choose
1
1
1
answer:
\newline
(A) Exactly one solution
\newline
(B) No solutions
\newline
(C) Infinitely many solutions
Get tutor help
How many solutions does the system have?
\newline
{
y
=
4
x
−
8
4
y
=
4
x
−
8
\left\{\begin{array}{l} y=4 x-8 \\ 4 y=4 x-8 \end{array}\right.
{
y
=
4
x
−
8
4
y
=
4
x
−
8
\newline
Choose
1
1
1
answer:
\newline
(A) Exactly one solution
\newline
(B) No solutions
\newline
(C) Infinitely many solutions
Get tutor help
How many solutions does the system have?
\newline
{
6
x
−
y
=
−
1
6
x
+
y
=
−
1
\left\{\begin{array}{l} 6 x-y=-1 \\ 6 x+y=-1 \end{array}\right.
{
6
x
−
y
=
−
1
6
x
+
y
=
−
1
\newline
Choose
1
1
1
answer:
\newline
(A) Exactly one solution
\newline
(B) No solutions
\newline
(C) Infinitely many solutions
Get tutor help
How many solutions does the system have?
\newline
{
8
x
+
2
y
=
14
8
x
+
2
y
=
4
\left\{\begin{array}{l} 8 x+2 y=14 \\ 8 x+2 y=4 \end{array}\right.
{
8
x
+
2
y
=
14
8
x
+
2
y
=
4
\newline
Choose
1
1
1
answer:
\newline
(A) Exactly one solution
\newline
(B) No solutions
\newline
(C) Infinitely many solutions
Get tutor help
How many solutions does the system have?
\newline
{
5
x
−
y
=
2
5
x
−
y
=
−
2
\left\{\begin{array}{l} 5 x-y=2 \\ 5 x-y=-2 \end{array}\right.
{
5
x
−
y
=
2
5
x
−
y
=
−
2
\newline
Choose
1
1
1
answer:
\newline
(A) Exactly one solution
\newline
(B) No solutions
\newline
(C) Infinitely many solutions
Get tutor help
How many solutions does the system have?
\newline
{
y
=
−
7
x
+
8
y
=
−
7
x
−
8
\left\{\begin{array}{l} y=-7 x+8 \\ y=-7 x-8 \end{array}\right.
{
y
=
−
7
x
+
8
y
=
−
7
x
−
8
\newline
Choose
1
1
1
answer:
\newline
(A) Exactly one solution
\newline
(B) No solutions
\newline
(C) Infinitely many solutions
Get tutor help
How many solutions does the system have?
\newline
{
2
y
=
4
x
+
6
y
=
2
x
+
6
\left\{\begin{array}{l} 2 y=4 x+6 \\ y=2 x+6 \end{array}\right.
{
2
y
=
4
x
+
6
y
=
2
x
+
6
\newline
Choose
1
1
1
answer:
\newline
(A) Exactly one solution
\newline
(B) No solutions
\newline
(C) Infinitely many solutions
Get tutor help
How many solutions does the system have?
\newline
{
y
=
5
x
+
1
y
=
−
2
x
−
8
\left\{\begin{array}{l} y=5 x+1 \\ y=-2 x-8 \end{array}\right.
{
y
=
5
x
+
1
y
=
−
2
x
−
8
\newline
Choose
1
1
1
answer:
\newline
(A) Exactly one solution
\newline
(B) No solutions
\newline
(C) Infinitely many solutions
Get tutor help
How many solutions does the system have?
\newline
{
3
x
+
y
=
8
2
x
+
2
y
=
8
\left\{\begin{array}{l} 3 x+y=8 \\ 2 x+2 y=8 \end{array}\right.
{
3
x
+
y
=
8
2
x
+
2
y
=
8
\newline
Choose
1
1
1
answer:
\newline
(A) Exactly one solution
\newline
(B) No solutions
\newline
(C) Infinitely many solutions
Get tutor help
How many solutions does the system have?
\newline
{
x
+
y
=
3
5
x
+
5
y
=
15
\left\{\begin{array}{l} x+y=3 \\ 5 x+5 y=15 \end{array}\right.
{
x
+
y
=
3
5
x
+
5
y
=
15
\newline
Choose
1
1
1
answer:
\newline
(A) Exactly one solution
\newline
(B) No solutions
\newline
(C) Infinitely many solutions
Get tutor help
How many solutions does the system have?
\newline
{
y
=
5
+
6
x
y
=
6
x
+
5
\left\{\begin{array}{l} y=5+6 x \\ y=6 x+5 \end{array}\right.
{
y
=
5
+
6
x
y
=
6
x
+
5
\newline
Choose
1
1
1
answer:
\newline
(A) Exactly one solution
\newline
(B) No solutions
\newline
(C) Infinitely many solutions
Get tutor help
2
y
+
16
=
10
x
4
x
−
L
y
=
8
−
x
\begin{array}{c} 2 y+16=10 x \\ 4 x-L y=8-x \end{array}
2
y
+
16
=
10
x
4
x
−
L
y
=
8
−
x
\newline
In the system of equations,
L
L
L
is a constant. For what value of
L
L
L
does the system of linear equations have infinitely many solutions?
Get tutor help
How many solutions does the system of equations below have?
\newline
y
=
3
x
−
9
y = 3x - 9
y
=
3
x
−
9
\newline
y
=
3
x
+
4
9
y = 3x + \frac{4}{9}
y
=
3
x
+
9
4
\newline
Choices:
\newline
(A)
no solution
\text{no solution}
no solution
\newline
(B)
one solution
\text{one solution}
one solution
\newline
(C)
infinitely many solutions
\text{infinitely many solutions}
infinitely many solutions
Get tutor help
