SOLUTION: 3x+4y=12 1x+4/3y=4

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Question 118518: 3x+4y=12
1x+4/3y=4
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


%281%29%2Ax%2B%284%2F3%29%2Ay=4 Start with the second equation


3%28%281%29%2Ax%2B%284%2F3%29%2Ay%29=%283%29%2A%284%29 Multiply both sides by the LCD 3



3%2Ax%2B4%2Ay=12 Distribute and simplify


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Lets start with the given system of linear equations

3%2Ax%2B4%2Ay=12
3%2Ax%2B4%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=12-3%2AxSubtract 3%2Ax from both sides

y=%2812-3%2Ax%29%2F4 Divide both sides by 4.


Which breaks down and reduces to



y=3-%283%2F4%29%2Ax Now we've fully isolated y

Since y equals 3-%283%2F4%29%2Ax we can substitute the expression 3-%283%2F4%29%2Ax into y of the 2nd equation. This will eliminate y so we can solve for x.


3%2Ax%2B4%2Ahighlight%28%283-%283%2F4%29%2Ax%29%29=12 Replace y with 3-%283%2F4%29%2Ax. Since this eliminates y, we can now solve for x.

3%2Ax%2B4%2A%283%29%2B4%28-3%2F4%29x=12 Distribute 4 to 3-%283%2F4%29%2Ax

3%2Ax%2B12-%2812%2F4%29%2Ax=12 Multiply



3%2Ax%2B12-3%2Ax=12 Reduce any fractions

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


3%2Ax-3%2Ax=0 Combine the terms on the right side



0%2Ax=0 Now combine the terms on the left side.
0=0 Since this expression is true for any x, we have an identity.


So there are an infinite number solutions. The simple reason is the 2 equations represent 2 lines that overlap each other. So they intersect each other at an infinite number of points.

If we graph 3%2Ax%2B4%2Ay=12 and 3%2Ax%2B4%2Ay=12 we get

+graph%28+500%2C+600%2C+-6%2C+5%2C+-10%2C+10%2C+%2812-3%2Ax%29%2F4%29+ graph of 3%2Ax%2B4%2Ay=12


+graph%28+500%2C+600%2C+-6%2C+5%2C+-10%2C+10%2C+%2812-3%2Ax%29%2F4+%29+ graph of 3%2Ax%2B4%2Ay=12 (hint: you may have to solve for y to graph these)

we can see that these two lines are the same. So this system is dependent