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Math Problems
Algebra 2
Find the number of solutions to a system of equations
Algebra
1
1
1
-Unit
3
3
3
: Two Variable Statistics EXIT TICKET Estimate Line of Best Fit
\newline
Name Aaron sams
\newline
Date:
\newline
\quad
\newline
\quad
\newline
Pd
\newline
\quad
\newline
\quad
Use a ruler to draw an approximate line of best fit thorough the points.
\newline
\newline
Slope:
1
,
0
1,0
1
,
0
\newline
\newline
Y-intercept:
\newline
\newline
Equation:
\newline
Positive or Negative Correlation?
\newline
Positive
\newline
Strong or Weak?
\newline
Strong
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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
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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?
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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
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Agnes, Betty and Cathy have
220
220
220
stamps altogether. Agnes has
3
3
3
times as many stamps as Betty. Cathy has
40
40
40
more stamps than Betty. How many stamps does Betty have?
\newline
(Draw models to help you.)
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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
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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
{
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
=
−
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
{
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
=
−
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
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