SOLUTION: Solve the system of equations:{3x+9y=7} {2x+6y=1}

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Question 92620: Solve the system of equations:{3x+9y=7}
{2x+6y=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

3%2Ax%2B9%2Ay=7
2%2Ax%2B6%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

9%2Ay=7-3%2AxSubtract 3%2Ax from both sides

y=%287-3%2Ax%29%2F9 Divide both sides by 9.


Which breaks down and reduces to



y=7%2F9-%281%2F3%29%2Ax Now we've fully isolated y

Since y equals 7%2F9-%281%2F3%29%2Ax we can substitute the expression 7%2F9-%281%2F3%29%2Ax into y of the 2nd equation. This will eliminate y so we can solve for x.


2%2Ax%2B6%2Ahighlight%28%287%2F9-%281%2F3%29%2Ax%29%29=1 Replace y with 7%2F9-%281%2F3%29%2Ax. Since this eliminates y, we can now solve for x.

2%2Ax%2B6%2A%287%2F9%29%2B6%28-1%2F3%29x=1 Distribute 6 to 7%2F9-%281%2F3%29%2Ax

2%2Ax%2B42%2F9-%286%2F3%29%2Ax=1 Multiply



2%2Ax%2B14%2F3-2%2Ax=1 Reduce any fractions

2%2Ax-2%2Ax=1-14%2F3 Subtract 14%2F3 from both sides


2%2Ax-2%2Ax=3%2F3-14%2F3 Make 1 into a fraction with a denominator of 3


2%2Ax-2%2Ax=-11%2F3 Combine the terms on the right side



0%2Ax=-11%2F3 Now combine the terms on the left side.
0%2F1=-11%2F3 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%28+500%2C+600%2C+-6%2C+5%2C+-10%2C+10%2C+%287-3%2Ax%29%2F9%2C+%281-2%2Ax%29%2F6+%29+ graph of 3%2Ax%2B9%2Ay=7 (red) and 2%2Ax%2B6%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