Question

Solve the following system by the substitution method. Show your work.

{2x−7y=12
−x+3.5y=−6

Answer 1

see the explanation

The system has infinity solutions

Explanation:

we have

`2x-7y=12` ----> equation A

`-x+3.5y=-6`

isolate the variable x

`x=3.5y+6` ----> equation B

Solve by the substitution method.

substitute equation B in equation A

`2(3.5y+6)-7y=12`

solve for y

`7y+12-7y=12\\12=12`

The system has infinity solutions

That means The equation A and equation B are the same line

Verify

we have

`2x-7y=12` ----> equation A

`-x+3.5y=-6` ----> equation B

Multiply by -2 both sides equation B

`(-2)(-x)+(-2)(3.5y)=-6(-2)`

`2x-7y=12`

so

Equation A and equation B is the same line

The system has infinity solutions