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What is the solution to the system of equations?

3x - 6y = -12

x - 2y = -8

(a) Use the substitution method to justify that the given system of equations has no solution.

(a) What do you know about the two lines in this system of equations?

Sagot :

Answer:

(a) Proof explained below

(b) The two lines are parallel

Step-by-step explanation:

(a) In the second equation express [tex]x[/tex] in terms of [tex]y[/tex] to get:

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

Then, substitute [tex]x[/tex] for [tex]2y-8[/tex] in the first equation to get:

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

Open parentheses using the distributive property ([tex]a(b-c)=ab-ac[/tex]) which results in:

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

Combine like terms to reach:

[tex]-24=-12[/tex], which is not true. Therefore, for any values of [tex]x[/tex] and [tex]y[/tex], the systems of equations will have no solutions.

Since the two lines have no solutions, that means that they are parallel.

Hope this helps :)

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