SOLUTION: solve each systems of equations algebraically 38. -3x+12y=6 2x-8y=6

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Question 120664: solve each systems of equations algebraically

38. -3x+12y=6
2x-8y=6
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
#38

Solved by pluggable solver: Solving a linear system of equations by subsitution


Lets start with the given system of linear equations

-3%2Ax%2B12%2Ay=6
2%2Ax-8%2Ay=6

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=6%2B3%2AxAdd 3%2Ax to both sides

y=%286%2B3%2Ax%29%2F12 Divide both sides by 12.


Which breaks down and reduces to



y=1%2F2%2B%281%2F4%29%2Ax Now we've fully isolated y

Since y equals 1%2F2%2B%281%2F4%29%2Ax we can substitute the expression 1%2F2%2B%281%2F4%29%2Ax into y of the 2nd equation. This will eliminate y so we can solve for x.


2%2Ax%2B-8%2Ahighlight%28%281%2F2%2B%281%2F4%29%2Ax%29%29=6 Replace y with 1%2F2%2B%281%2F4%29%2Ax. Since this eliminates y, we can now solve for x.

2%2Ax-8%2A%281%2F2%29-8%281%2F4%29x=6 Distribute -8 to 1%2F2%2B%281%2F4%29%2Ax

2%2Ax-8%2F2-%288%2F4%29%2Ax=6 Multiply



2%2Ax-4-2%2Ax=6 Reduce any fractions

2%2Ax-2%2Ax=6%2B4Add 4 to both sides


2%2Ax-2%2Ax=10 Combine the terms on the right side



0%2Ax=10 Now combine the terms on the left side.
0%2F1=10%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 -3%2Ax%2B12%2Ay=6 (red) and 2%2Ax-8%2Ay=6 (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