Question

Which statements are true regarding the system of equations?check all that apply​

Answer 1

Answer:

They are parallel

Their slopes are equal

Y intercepts are different

System has no solution

Step-by-step explanation:

Answer 2

Answer:

The statements which are  true regarding the system of equations is:

• The lines are parallel.

• The slopes are equal.

• The y-intercepts are different.

• The system has no solution.

Step-by-step explanation:

The equation of a line in slope-intercept form is given by:

             $y=mx+c$

where m is the slope of the line and c is the y-intercept of a line.

The first equation is:

$8x+10y=30$

i.e. on converting this equation to slope-intercept form we get:

$10y=30-8x$

i.e.

$y=\dfrac{30}{10}-\dfrac{8x}{10}\\\\i.e.\\\\y=-0.8x+3$

The slope of first line is: -0.8

and y-intercept is: 3

and the second equation is:

$12x+15y=60$

i.e. on converting this equation to slope-intercept form we get:

$y=\dfrac{-12}{15}x+\dfrac{60}{15}\\\\\\y=-0.8x+4$

The slope of second line is: -0.8

and y-intercept is: 4

Since, the slope of both the line are equal (i.e. -0.8)

This means that the two lines are parallel and hence they will never coincide.

Hence, the system has no solution.

Also, the y-intercepts are different.