Question

Which statements are true regarding the system of equations? Check all that apply. 8 x + 10 y = 30. 12 x + 15 y = 60. The lines coincide. The lines are parallel. The slopes are equal. The y-intercepts are different. The system has one solution. The system has an infinite number of solutions. The system has no solution. Mark this and return

Answer 1

Answer: The lines are parallel.

The slopes are equal.

The y-intercepts are different.

The system has no solution.

Step-by-step explanation:

For a pair of equations:

They coincide if

They are parallel if

They intersect if

Given equations:

Here,

⇒

Hence, The lines are parallel.

It has no solution. [parallel lines have no solution]

Write 8 x + 10 y = 30 in the form of y= mx+c, where m is slope and c is the y-intercept.

i.e. slope of 8 x + 10 y = 30 is -0.8 and y-intercept =3

Write 12 x + 15 y = 60 in the form of y= mx+c, where m is slope

i.e. slope of 12 x + 15 y = 60 is -0.8 and y-intercept =4

i.e. The slopes are equal but y-intercepts are different.

Answer 2

Answer: The lines are parallel.

The slopes are equal.

The y-intercepts are different.

The system has no solution.

Explanation:

For a pair of equations:
`a_1x+b_1y=c_1\\\\a_2x+b_2y=c_2`

They coincide if
`(a_1)/(a_2)=(b_1)/(b_2)=(c_1)/(c_2)`

They are parallel if
`(a_1)/(a_2)=(b_1)/(b_2)\\eq(c_1)/(c_2)`

They intersect if
`(a_1)/(a_2)\\eq(b_1)/(b_2)`

Given equations:
`8 x + 10 y = 30\\ 12 x + 15 y = 60`

Here,

`(a_1)/(a_2)=(8)/(12)=(2)/(3)\\\\ (b_1)/(b_2)=(10)/(15)=(2)/(3)\\\\ (c_1)/(c_2)=(30)/(60)=(1)/(2)`

⇒
`(a_1)/(a_2)=(b_1)/(b_2)\\eq(c_1)/(c_2)`

Hence, The lines are parallel.

It has no solution. [parallel lines have no solution]

Write 8 x + 10 y = 30 in the form of y= mx+c, where m is slope and c is the y-intercept.

`y=-(8)/(10)x+(30)/(10)\Rightarrow\ y=-0.8x+3`

i.e. slope of 8 x + 10 y = 30 is -0.8 and y-intercept =3

Write 12 x + 15 y = 60 in the form of y= mx+c, where m is slope

`y=-(12)/(15)x+(60)/(15)\Rightarrow\ y=-0.8x+4`

i.e. slope of 12 x + 15 y = 60 is -0.8 and y-intercept =4

i.e. The slopes are equal but y-intercepts are different.