AnswersAlgebra III ASolving Systems of Linear Equations: Graphing

Solving Systems of Linear Equations: Graphing Answers

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A coordinate grid with 2 lines. The first line labeled f(x) passes through (negative 3, 3), (0, 2), and (3, 1). The second line labeled g(x) passes through the points at (negative 3, 0) and (0, 2)

Question illustration
A
(–3, 0)
B
(–3, 3)
C
(0, 2)
D
(3, 1)
2
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A coordinate grid with a line labeled y equals StartFraction 2 over 5 EndFraction x minus 5 passing through the points (negative 5, negative 7) and (0, negative 5)

Question illustration
A
x – y =
Option A
B
x – y =
Option B
C
x – y =
Option C
D
x – y =
Option D
3

Which values of m and b will create a system of equations with no solution? Select two options.y = mx + b y = –2x + m = –3 and b = m = –2 and b = m = 2 and b = m = and b = m = -2 and b =

Question illustration
A
m = –3 and b =
Option A
B
m = –2 and b =
Option B
C
m = 2 and b =
Option C
D
m = and b =
Option D
E
m = -2 and b =
Option E
4

Billy graphed the system of linear equations to find an approximate solution.y = x + y = x – 3Which points are possible approximations for this system? Select two options.(1.9, 2.5)(2.2, –1.4)(2.2, –1.35)(1.9, 2.2)(1.9, 1.5)

Question illustration
A
(1.9, 2.5)
B
(2.2, –1.4)
C
(2.2, –1.35)
D
(1.9, 2.2)
E
(1.9, 1.5)
5

How many solutions does this linear system have?y = 2x – 5 –8x – 4y = –20

A
one solution: (–2.5, 0)
B
one solution: (2.5, 0)
C
no solution
D
infinite number of solutions
6

Sylvie finds the solution to the system of equations by graphing.y = x + 1 and y = x – 1Which graph shows the solution to Sylvie’s system of equations?

Question illustration
A
Option
B
Option
C
Option
D
Option
7

y=–x + 4x + 2y=–8

Question illustration
A
one solution: (8, 0)
B
one solution: (0, 8)
C
no solution
D
infinite number of solutions
8

What value of b will cause the system to have an infinite number of solutions?

Question illustration
A
-6
B
-3
C
3
D
6
9

A system of equations has no solution. If y = 8x + 7 is one of the equations, which could be the other equation?

A
2y = 16x +14
B
y = 8x – 7
C
y = –8x + 7
D
2y = −16x − 14
10

What value of b will make the system of equations have an infinite number of solutions?y = -2x + b 4x + 2y = 8

A
2
B
8
C
4
D
-4
11

How many solutions does this linear system have?y = 2x – 5 –8x – 4y = –20

A
one solution: (–2.5, 0)
B
one solution: (2.5, 0)
C
no solution
D
infinite number of solutions
12

y=–x + 4x + 2y=–8

Question illustration
A
one solution: (8, 0)
B
one solution: (0, 8)
C
no solution
D
infinite number of solutions
13

Sylvie finds the solution to the system of equations by graphing.y = x + 1 and y = x – 1Which graph shows the solution to Sylvie’s system of equations?

Question illustration
A
Option
B
Option
C
Option
D
Option
14

What value of b will make the system of equations have an infinite number of solutions?y = -2x + b 4x + 2y = 8

A
2
B
8
C
4
D
-4
15

Billy graphed the system of linear equations to find an approximate solution.y = x + y = x – 3Which points are possible approximations for this system? Select two options.

Question illustration
A
(1.9, 2.5)
B
(2.2, –1.4)
C
(2.2, –1.35)
D
(1.9, 2.2)
E
(1.9, 1.5)
16

y=–6x+2–12x – 2y=–4

A
one solution: (0, 0)
B
one solution: (1, –4)
C
no solution
D
infinite number of solutions
17

What is the solution to the system of equations?2x – y = 7y = 2x + 3

A
(2, 3)
B
(2, 7)
C
no solution
D
infinite number of solutions
18

A coordinate grid with 2 lines. The first line is labeled y equals negative StartFraction 7 over 4 EndFraction x plus StartFraction 5 over 2 EndFraction and passes through the (0, 2.5) and (2.2, negative 1.4). The second line is labeled y equals StartFraction 3 over 4 EndFraction x minus 3 and passes through (0, negative 3, 0.14) and (2.2, negative 1.4)

Question illustration
A
(0.33, 1)
B
(1.33, 1)
C
(1.83, 1)
D
(2.33, 1)
19

A coordinate grid with one line labeled 3 y equals 2 x minus 9. The line passes through points at (0, negative 3) and (3, negative 1).

Question illustration
A
2y = x – 4.5
B
y = x – 3
Option B
C
6y = 6x – 27
D
y = x – 4.5
Option D
20

Which values of m and b will create a system of equations with no solution? Select two options.y = mx + b y = –2x +

Question illustration
A
m = –3 and b =
Option A
B
m = –2 and b =
Option B
C
m = 2 and b =
Option C
D
m = and b =
Option D
E
m = -2 and b =
Option E

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