SOLUTION: This question confused me. 2(x+1)-(y-4)=15 3(x-1)+4(y+2)=2

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Question 174867: This question confused me.
2(x+1)-(y-4)=15
3(x-1)+4(y+2)=2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
2%28x%2B1%29-%28y-4%29=15 Start with the first equation.


2x%2B2-y%2B4=15 Distribute


2x-y%2B6=15 Combine like terms.


2x-y=15-6 Subtract 6 from both sides.


2x-y=9 Combine like terms.


---------------------------------------------------


3%28x-1%29%2B4%28y%2B2%29=2 Move onto the second equation.


3x-3%2B4y%2B8=2 Distribute


3x%2B4y%2B5=2 Combine like terms.


3x%2B4y=2-5 Subtract 5 from both sides.


3x%2B4y=-3 Combine like terms.



==================================================================






So we have the system of equations:

system%282x-y=9%2C3x%2B4y=-3%29


Let's solve this system by substitution


Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.


So let's isolate y in the first equation

2x-y=9 Start with the first equation


-y=9-2x Subtract 2x from both sides


-y=-2x%2B9 Rearrange the equation


y=%28-2x%2B9%29%2F%28-1%29 Divide both sides by -1


y=%28%28-2%29%2F%28-1%29%29x%2B%289%29%2F%28-1%29 Break up the fraction


y=2x-9 Reduce



---------------------

Since y=2x-9, we can now replace each y in the second equation with 2x-9 to solve for x



3x%2B4highlight%28%282x-9%29%29=-3 Plug in y=2x-9 into the second equation. In other words, replace each y with 2x-9. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



3x%2B%284%29%282%29x%2B%284%29%28-9%29=-3 Distribute 4 to 2x-9


3x%2B8x-36=-3 Multiply


11x-36=-3 Combine like terms on the left side


11x=-3%2B36Add 36 to both sides


11x=33 Combine like terms on the right side


x=%2833%29%2F%2811%29 Divide both sides by 11 to isolate x



x=3 Divide





-----------------First Answer------------------------------


So the first part of our answer is: x=3









Since we know that x=3 we can plug it into the equation y=2x-9 (remember we previously solved for y in the first equation).



y=2x-9 Start with the equation where y was previously isolated.


y=2%283%29-9 Plug in x=3


y=6-9 Multiply


y=-3 Combine like terms



-----------------Second Answer------------------------------


So the second part of our answer is: y=-3









-----------------Summary------------------------------

So our answers are:

x=3 and y=-3

which form the ordered pair


This means that the system is consistent and independent.








Now let's graph the two equations (if you need help with graphing, check out this solver)


From the graph, we can see that the two equations intersect at . This visually verifies our answer.




graph of 2x-y=9 (red) and 3x%2B4y=-3 (green) and the intersection of the lines (blue circle).