Question

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

Answer 1

Answer:

see the explanation

The system has infinity solutions

Step-by-step 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