What is the solution to the system of equations? 3x-6y=-12 " " x-2y=10 Use the substitution method to justify that the given system of equations has no solution. What do you know about the two lines in this system of equations?

If the system of linear equations has one solution, then the two line are intersected
If the system of linear equations has no solution, then the two line are parallel
If the system of linear equations has many solutions, then the two line are coincide (over each other)

∵ The system of equation is

3x - 6y = -12 ⇒ (1)

x - 2y = 10 ⇒ (2)

To solve the system using the substitution method, find x in terms of y in equation (2)

∵ x - 2y = 10

- Add 2y to both sides

∴ x = 2y + 10 ⇒ (3)

Substitute x in equation (1) by equation (3)

∵ 3(2y + 10) - 6y = -12

- Simplify the left hand side

∴ 6y + 30 - 6y = -12

- Add like terms in the left hand side

∴ 30 = -12

∴ The left hand side ≠ the right hand side

∴ There is no solution for the system of equations

∴ The system of equations represents two parallel lines

The two lines in this system of equations are parallel

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edenbasipov edenbasipov · Answer 2 · 2021-07-22T22:52:58+02:00

Answer:

A.

x-2y=-8

x=-8+2y

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

-24+6y-6y=-12

-24=-12

Therefore, because -24 is not equal to -12, there is no solution.

B.

The system of equations is parallel because they have no solution.

Step-by-step explanation:

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