SOLUTION: I am trying to solve these equations by substitution or elimination amd then I have to interpret the result. Each time I do it, my solution comes out to 0. Can someone help me un

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Question 94383: I am trying to solve these equations by substitution or elimination amd then I have to interpret the result. Each time I do it, my solution comes out to 0. Can someone help me understand this?
2x+4y=10
3x+6y=12
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

2%2Ax%2B4%2Ay=10
3%2Ax%2B6%2Ay=12

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

4%2Ay=10-2%2AxSubtract 2%2Ax from both sides

y=%2810-2%2Ax%29%2F4 Divide both sides by 4.


Which breaks down and reduces to



y=5%2F2-%281%2F2%29%2Ax Now we've fully isolated y

Since y equals 5%2F2-%281%2F2%29%2Ax we can substitute the expression 5%2F2-%281%2F2%29%2Ax into y of the 2nd equation. This will eliminate y so we can solve for x.


3%2Ax%2B6%2Ahighlight%28%285%2F2-%281%2F2%29%2Ax%29%29=12 Replace y with 5%2F2-%281%2F2%29%2Ax. Since this eliminates y, we can now solve for x.

3%2Ax%2B6%2A%285%2F2%29%2B6%28-1%2F2%29x=12 Distribute 6 to 5%2F2-%281%2F2%29%2Ax

3%2Ax%2B30%2F2-%286%2F2%29%2Ax=12 Multiply



3%2Ax%2B15-3%2Ax=12 Reduce any fractions

3%2Ax-3%2Ax=12-15 Subtract 15 from both sides


3%2Ax-3%2Ax=-3 Combine the terms on the right side



0%2Ax=-3 Now combine the terms on the left side.
0%2F1=-3%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 2%2Ax%2B4%2Ay=10 (red) and 3%2Ax%2B6%2Ay=12 (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