SOLUTION: Solve the following system by substitution 4x-12y=5 -x+3y=-1

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Question 120681: Solve the following system by substitution
4x-12y=5
-x+3y=-1
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

4%2Ax-12%2Ay=5
-1%2Ax%2B3%2Ay=-1

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

-12%2Ay=5-4%2AxSubtract 4%2Ax from both sides

y=%285-4%2Ax%29%2F-12 Divide both sides by -12.


Which breaks down and reduces to



y=-5%2F12%2B%281%2F3%29%2Ax Now we've fully isolated y

Since y equals -5%2F12%2B%281%2F3%29%2Ax we can substitute the expression -5%2F12%2B%281%2F3%29%2Ax into y of the 2nd equation. This will eliminate y so we can solve for x.


-1%2Ax%2B3%2Ahighlight%28%28-5%2F12%2B%281%2F3%29%2Ax%29%29=-1 Replace y with -5%2F12%2B%281%2F3%29%2Ax. Since this eliminates y, we can now solve for x.

-1%2Ax%2B3%2A%28-5%2F12%29%2B3%281%2F3%29x=-1 Distribute 3 to -5%2F12%2B%281%2F3%29%2Ax

-1%2Ax-15%2F12%2B%283%2F3%29%2Ax=-1 Multiply



-1%2Ax-5%2F4%2B1%2Ax=-1 Reduce any fractions

-1%2Ax%2B1%2Ax=-1%2B5%2F4Add 5%2F4 to both sides


-1%2Ax%2B1%2Ax=-4%2F4%2B5%2F4 Make -1 into a fraction with a denominator of 4


-1%2Ax%2B1%2Ax=1%2F4 Combine the terms on the right side



0%2Ax=1%2F4 Now combine the terms on the left side.
0%2F1=1%2F4 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 4%2Ax-12%2Ay=5 (red) and -1%2Ax%2B3%2Ay=-1 (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