Question

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

y=−x+1
2y=−2x+2

Answer 1

take a look at ur graph....notice that for 2 equations u have 1 line....this means that ur equations have the same line...they are on top of each other...this means they are coincident equations.....coincident equations have infinite solutions....and if they have at least 1 solution they are consistent...so ur answer is coincident and consistent

Answer 2

The system of equations is consistent and coincident

Explanation:

A system of equations is consistent if it has at least one solution. The system is consistent and coincident if it has a solutions but the number of solutions are infinite. The system is inconsistent if it has no solution.

From your equation we have:

Y= −X+1 (1)

2Y= −2X+2 (2)

Replacing (1) in (2)

2(-X +1 )= -2X + 2

-2X +2 = -2X +2

When we arrive at this type of answer, the equality is satisfied no matter which value X takes. Any X value solves the equations so any pair of (X,Y) values is a solution of the so the system of equations is consistent and coincident. Graphically, as shown in your graph this means that the graphs of both functions interlap in all points.