Question

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

Answer 1

They are parallel

Their slopes are equal

Y intercepts are different

System has no solution

Explanation:

Answer 2

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.

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=(30)/(10)-(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=(-12)/(15)x+(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.