Is the system of equations is consistent, consistent and coincident, or inconsistent?

y=−3x+12y=−6x+2

consistent

Step-by-step explanation:

Here we are given two equations.

Y = -3x + 12

Y  = -6x + 2

First let's see the definition of consistent and inconsistent.

If a system has at least one solution, it is said to be consistent .

If a consistent system has exactly one solution, it is independent .

If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line.

If a system has no solution, it is said to be inconsistent . The graphs of the lines do not intersect, so the graphs are parallel and there is no solution.

Let's solve this equations

-3x + 12 = -6x + 2

6x - 3x = 2 -12

3x = -10

x = -10/3

Now plug in x = -10/3 in the first equation to get the value of y.

y = -3*-10/3 + 12

y = 10 + 12

y = 22

Therefore, the system has exactly one solution at (-10/3, 22).

If a system has at least one solution, it is said to be consistent .

Therefore, answer is consistent.

Hope this will helpful.

Thank you.