SOLUTION: Solve the system by the substitution method. x – y = –3 x – y = 4 Thank you.

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Question 111779: Solve the system by the substitution method.
x – y = –3
x – y = 4
Thank you.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Solving a linear system of equations by subsitution


Lets start with the given system of linear equations

1%2Ax-1%2Ay=-3
1%2Ax-1%2Ay=4

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

-1%2Ay=-3-1%2AxSubtract 1%2Ax from both sides

y=%28-3-1%2Ax%29%2F-1 Divide both sides by -1.


Which breaks down and reduces to



y=3%2B1%2Ax Now we've fully isolated y

Since y equals 3%2B1%2Ax we can substitute the expression 3%2B1%2Ax into y of the 2nd equation. This will eliminate y so we can solve for x.


1%2Ax%2B-1%2Ahighlight%28%283%2B1%2Ax%29%29=4 Replace y with 3%2B1%2Ax. Since this eliminates y, we can now solve for x.

1%2Ax-1%2A%283%29-1%281%29x=4 Distribute -1 to 3%2B1%2Ax

1%2Ax-3-1%2Ax=4 Multiply



1%2Ax-3-1%2Ax=4 Reduce any fractions

1%2Ax-1%2Ax=4%2B3Add 3 to both sides


1%2Ax-1%2Ax=7 Combine the terms on the right side



0%2Ax=7 Now combine the terms on the left side.
0%2F1=7%2F1 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.


graph of 1%2Ax-1%2Ay=-3 (red) and 1%2Ax-1%2Ay=4 (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 inconsistent