Question

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

(equation) v
y = y equals StartFraction 1 over 3 EndFraction x minus 4.x – 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:

a. The system has one solution.

e. The equations represent the same line

Answer 2

The correct option are  option b and c

b. The system consists parallel solution.

c.Both lines have the same slope.

Step-by-step explanation:

Slope :

The ratio of change y co-ordinate to x   co-ordinate. It is also known as gradient.

Slope(m) =  tan θ  $=\frac{y_2-y_1}{x_2-x_1}$

where θ angle between the line and positive x-axis.

If a line is in the form y= mx+c

Then the slope of the line is m.

If the slopes of two line are equal, the the lines are parallel to each other.

If the product of the slopes equal to -1, then the lines perpendicular to each other.

Given equation of straight lines are

$y= \frac{1}{3}x-4$ ......(1)                

3y-x=-7

$\Rightarrow 3y=x-7$

$\Rightarrow y=\frac{1}{3}x-\frac73$........(2)

The slope of the lines is $=\frac13$

c.Both lines have the same slope.

The lines are parallel.Since the slopes are equal.

b. The system consists parallel solution.