Question

Heather writes the equations below to represent two lines drawn on the coordinate plane. –6x + 18y = 0 4x – 12y = 20 After applying the linear combination method, Heather arrived at the equation 0 = 60. What conclusion can be drawn about the system of equations? The equation has no solution; therefore, the system of equations has no solution. The equation has a solution at (0, 60); therefore, the system of equations has a solution at (0, 60). The equation has infinite solutions; therefore, the system of equation as infinite solutions. The equation has a solution at (0, 0); therefore, the system of equations has a solution at (0, 0).

Answer 1

The equation has no solution; therefore, the system of equations has no solution.

Explanation:

A on edg

Answer 2

The equation has no solution; therefore, the system of equations has no solution

Explanation:

we have

`-6x+18y=0` -----> equation A

`4x-12y=20` -----> equation B

we know that

If after applying the linear combination method, Heather arrived at the equation 0 = 60

then

The reason is because both lines are parallel, therefore the system of equations has no solutions

Verify

isolate the variable y in the equation A

`18y=6x`

`y=(1/3)x` --------> the slope is 1/3

isolate the variable y in the equation B

`12y=4x-20`

`y=(1/3)x-(20/12)`

`y=(1/3)x-(5/3)` --------> the slope is 1/3

Remember that

If the slopes are equal the lines are parallel

so

The system of equations has no solutions