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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?

Respuesta :

calculista

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

[tex]3x-6y=-12[/tex] ----> equation A

[tex]x-2y=-8[/tex] ----> equation B

Isolate the variable x in the equation B

[tex]x=2y-8[/tex]

Substitute the value of x in the equation A

[tex]3(2y-8)-6y=-12[/tex]

[tex]6y-24-6y=-12[/tex]

[tex]-24=-12[/tex] ------> 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?

[tex]3x-6y=-12[/tex] ------> equation A

isolate the variable y

[tex]6y=3x+12[/tex]

[tex]y=(1/2)x+2[/tex]

[tex]x-2y=-8[/tex] -------> equation B

isolate the variable y

[tex]2y=x+8[/tex]

[tex]y=(1/2)x+4[/tex]

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