Question

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

Answer 1

Answer:

B) The system consists of parallel lines.

C) Both lines have the same slope

Step-by-step 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.

Answer 2

Answer: Option B and Option C

Step-by-step explanation:

We must solve the following system of equations

$y = \frac{1}{3}x - 4\\3y = -7+x$

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

$-3y = -x +12$

$3y = -7+x$

-------------------------------------------                

$0 = 0x + 5$

$0=5$

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

By definition parallel lines have equal slopes