Answer:
The statements which are true regarding the system of equations is:
- 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:
[tex]y=mx+c[/tex]
where m is the slope of the line and c is the y-intercept of a line.
The first equation is:
[tex]8x+10y=30[/tex]
i.e. on converting this equation to slope-intercept form we get:
[tex]10y=30-8x[/tex]
i.e.
[tex]y=\dfrac{30}{10}-\dfrac{8x}{10}\\\\i.e.\\\\y=-0.8x+3[/tex]
The slope of first line is: -0.8
and y-intercept is: 3
and the second equation is:
[tex]12x+15y=60[/tex]
i.e. on converting this equation to slope-intercept form we get:
[tex]y=\dfrac{-12}{15}x+\dfrac{60}{15}\\\\\\y=-0.8x+4[/tex]
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.
