Question 84478: Solve system by substitution method. Determine whether the equation is dependent or inconsistent
2x-y=4
2x-y=3
Answer by funmath(2933)   (Show Source):
You can put this solution on YOUR website! Solve system by substitution method. Determine whether the equation is dependent or inconsistent
2x-y=4 R1
2x-y=3 R2
Before you even try to solve this equation, you can tell it's inconsistent because the left sides of both equations are the same, but the left side is different. However, let's try to solve it anyways.
Solve R1 for y:
2x-2x-y=-2x+4
-y=-2x+4
-(-y)=-(-2x+4)
y=2x-4
Now substitute what you got into R2 for y and try to solve for x:
2x-(2x-4)=3
2x-2x+4=3
4=3
The variables were eliminated and 4 doesn't =3, so it's inconsistent and has no solution.
Graphically, these are two parallel lines that will never intersect to give a solution.
Happy Calculating!!!
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