Question

Which statements about the system are true? Select two options.

y = 1/3x – 4

3y – x = –7

A) The system has one solution.
B) The system consists of parallel lines.
C) Both lines have the same slope.
D) Both lines have the same y–intercept.
E) The equations represent the same line.

Answer 1

Answer: Option B and Option C

Explanation:

We must solve the following system of equations

`y = (1)/(3)x - 4\\3y = -7+x`

To solve the system multiply at first equation by -3 and add it to the second equation

`-3y = -x +12`

`3y = -7+x`

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`0 = 0x + 5`

`0=5`

The system has no solution. Then both lines are parallel.

By definition parallel lines have equal slopes

Answer 2

B) The system consists of parallel lines.

C) Both lines have the same slope

Explanation:

we have

y=(1/3)x-4 -----> equation A

3y-x=-7

isolate the variable y

3y=x-7

y=(1/3)x-7 ----> equation B

Compare the equations

Line A and Line B have the same slope and different y-intercept

so

The system has no solution

The lines do not intersect

therefore

The system consists of parallel lines

Both lines have the same slope.