SOLUTION: 2x-y=4 2x-y=3
Coordinate Systems and Linear Equations
-> SOLUTION: 2x-y=4 2x-y=3
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Solving a linear system of equations by subsitution
Lets start with the given system of linear equations
Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to choose y.
Solve for y for the first equation
from both sides
Divide both sides by -1.
Which breaks down and reduces to
Now we've fully isolated y
Since y equals
we can substitute the expression
into y of the 2nd equation. This will eliminate y so we can solve for x.
Replace y with
. Since this eliminates y, we can now solve for x.
Distribute -1 to
Reduce any fractions
from both sides
Combine the terms on the right side
Now combine the terms on the left side.
Since this expression is not true, we have an inconsistency.
So there are no solutions. The simple reason is the 2 equations represent 2 parallel lines that will never intersect. Since no intersections occur, no solutions exist.
(green) (hint: you may have to solve for y to graph these)
and we can see that the two equations are parallel and will never intersect. So this system is