Question

What is the solution to the system of equations? 3x-6 = -12
x-2y = -8

(a) Use the substitution method to justify that the given system of equations has no solution.
(b) What do you know about the two lines in this system of equations?

Answer 1

Answer:

Part a) In the procedure

Part b) Line A and Line B are different parallel lines

Step-by-step explanation:

Part a) we have

$3x-6y=-12$ ----> equation A

$x-2y=-8$ ----> equation B

Isolate the variable x in the equation B

$x=2y-8$

Substitute the value of x in the equation A

$3(2y-8)-6y=-12$

$6y-24-6y=-12$

$-24=-12$ ------> is not true

therefore

The system of equations has no solutions

Part b) What do you know about the two lines in this system of equations?

$3x-6y=-12$ ------> equation A

isolate the variable y

$6y=3x+12$

$y=(1/2)x+2$

$x-2y=-8$ -------> equation B

isolate the variable y

$2y=x+8$

$y=(1/2)x+4$

Line A and Line B are parallel lines, because their slopes are the same

Line A and Line B are different lines because their y-intercept is not the same