SOLUTION: system of linear equations in two variables using substitution please help me solve these equation: x-y=3 6x+8y= -38 solve for x (note: both equations are together, noth s

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Question 147205This question is from textbook Alebra 2
: system of linear equations in two variables using substitution
please help me solve these equation: x-y=3 6x+8y= -38 solve for x
(note: both equations are together, noth separate problems)
 This question is from textbook Alebra 2

Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!


Start with the given system of equations:

system%28x-y=3%2C6x%2B8y=-38%29



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

x-y=3 Start with the first equation


-y=3-x Subtract x from both sides


-y=-x%2B3 Rearrange the equation


y=%28-x%2B3%29%2F%28-1%29 Divide both sides by -1


y=%28%28-1%29%2F%28-1%29%29x%2B%283%29%2F%28-1%29 Break up the fraction


y=x-3 Reduce



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

Since y=x-3, we can now replace each y in the second equation with x-3 to solve for x



6x%2B8highlight%28%28x-3%29%29=-38 Plug in y=x-3 into the second equation. In other words, replace each y with x-3. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



6x%2B%288%29%281%29x%2B%288%29%28-3%29=-38 Distribute 8 to x-3


6x%2B8x-24=-38 Multiply


14x-24=-38 Combine like terms on the left side


14x=-38%2B24Add 24 to both sides


14x=-14 Combine like terms on the right side


x=%28-14%29%2F%2814%29 Divide both sides by 14 to isolate x



x=-1 Divide





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


So the first part of our answer is: x=-1









Since we know that x=-1 we can plug it into the equation y=x-3 (remember we previously solved for y in the first equation).



y=x-3 Start with the equation where y was previously isolated.


y=%28-1%29-3 Plug in x=-1


y=-1-3 Multiply


y=-4 Combine like terms



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


So the second part of our answer is: y=-4









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

So our answers are:

x=-1 and y=-4

which form the point








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 x-y=3 (red) and 6x%2B8y=-38 (green) and the intersection of the lines (blue circle).


Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
solve these equation: x-y=3 6x+8y= -38 solve for x
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y = x-3
y = (-3/4)x - (19/4)
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Substitute to get:
x-3 = (-3/4)x - (19/4)
(7/4)x = -7/4
x = -1
------------
Substitute:
y = -1-3 = -4
-----------
Cheers,
Stan H.