Question

y = A system of equations. y equals StartFraction one-half EndFraction x minus 6. x equals negative 4.x – 6
x = –4
What is the solution to the system of equations?

(–8, –4)
(–4, –8)
(–4, 4)
(4, –4)

The tables represent two linear functions in a system.

A 2 column table with 5 rows. The first column, x, has the entries, negative 4, negative 2, 0, 2. The second column, y, has the entries, 26, 18, 10, 2. A 2 column table with 5 rows. The first column, x, has the entries, negative 4, negative 2, 0, 2. The second column, y, has the entries, 14, 8, 2, negative 4.
What is the solution to this system?

(1, 0)
(1, 6)
(8, 26)
(8, –22)

What is the solution to the system of equations?

y = A system of equations. y equals StartFraction one-third EndFraction minus 10. 2 x plus y equals 4.x – 10

2x + y = 4

(–8, 6)
(–6, 16)
(6, –8)
(16, –6)

What is the solution to the system of equations?

y = A system of equations. y equals StartFraction 2 over 3 EndFraction x plus 3. x equals negative 2.x + 3

x = –2

(negative 2, negative StartFraction 15 over 2 EndFraction)
(negative 2, StartFraction 5 over 3 EndFraction)
(negative 2, StartFraction 11 over 6 EndFraction)
(negative 2, StartFraction 13 over 3 EndFraction)

The tables represent two linear functions in a system.

A 2 column table with 5 rows. The first column, x, has the entries, negative 6, negative 3, 0, 3. The second column, y, has the entries, negative 22, negative 10, 2, 14. A 2 column table with 5 rows. The first column, x, has the entries, negative 6, negative 3, 0, 3. The second column, y, has the entries, negative 30, negative 21, negative 12, negative 3.
What is the solution to this system?

(negative StartFraction 13 over 3 EndFraction, negative 25)
(negative StartFraction 14 over 3 EndFraction, negative 54)
(–13, –50)
(–14, –54)

Ernesto tried to determine the solution for the system of equations using substitution. His work is shown below.

x – y = 7

3x – 2y = 8

Step 1: x = y + 7
Step 2: 3(y + 7) – 2y = 8
Step 3: 3y + 7 – 2y = 8
Step 4: y + 7 = 8
Step 5: y = 1

In which step did Ernesto make the first error?

Step 1
Step 2
Step 3
Step 4

y = –3x + 6
y = 9
What is the solution to the system of equations?

(–21, 9)
(9, –21)
(–1, 9)
(9, –1)

What is the solution to the system of equations?

y = 1.5x – 4

y = –x

(–1.6, 1.6)
(–1.5, 1.5)
(1.5, –1.5)
(1.6, –1.6)

What is the solution to the system of equations?

y = –3x – 2

5x + 2y = 15

(–40, 19)
(–19, 55)
(19, –40)
(55, –19)

Which value, when placed in the box, would result in a system of equations with infinitely many solutions?

y = -2x + 4

6x + 3y =

-12
-4
4
12

Answer 1

Here are the answers in order:

1) (-4, -8)
2) (8, -22)
3) (6, -8)
4) (-2, 5/3)
5) (-14, -54)
6) Step 3
7) (-1, 9)
8) (1.6, -1.6)
9) (-19, 55)
10) 12