In the solution of the system of equations, what is the value of x?
2x-4y=14
x+2y=7
a) -7
b) 7
c) 0
d) no solution

Question

In the solution of the system of equations, what is the value of x?
2x-4y=14
x+2y=7
a) -7
b) 7
c) 0
d) no solution

amistre64 · Answer

what happens when we test them out?

anonymous · Answer

I don't really understand what the question is asking of me because I don't know what the system of equations is, but I put in the answers for x and for a) y=-7, 7 for b) y=0
I'm not sure how to go about this at all, I don't think I'm finding the right thing...

jim_thompson5910 · Answer

In the first equation, we have -4y

In the second equation, we have 2y

Add them to get -4y + 2y = -2y

this is not 0y like we want, but we can easily fix that

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The coefficients of the y terms must be equal but opposite in sign so when we add the y terms, they cancel out

so we can double the 2y to get 4y. Notice how -4y + 4y = 0y = 0 so the y terms go away now

we have to multiply EVERY term in the second equation by 2 to make sure things balance out

jim_thompson5910 · Answer

So multiply everything in x+2y=7 by 2 to get 2x+4y = 14

jim_thompson5910 · Answer

we have this new system

2x-4y=14
2x+4y=14

Now add the equations


2x-4y=14
2x+4y=14
----------
4x+0y = 28

If 4x = 28, then x = ??

amistre64 · Answer

if we get the same y value for a given x value, then the solution to the system is (x,y)

notice that when x=7

2(7) -4y=14
  (7) +2y=7


14 -4y=14
  7 +2y=7


-4y=0
  2y=0

then for each equation y=0,  they have the solution point (7,0) tht satisfies both of them at the same time.

amistre64 · Answer

hence:

"I put in the answers for x and 
      for a) y=-7, 7   y has 2 values, so its not a solution
       for b) y=0        y has 1 value. it is common to both

amistre64 · Answer

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amistre64 · Answer

when x = x1,  y=y1 or y2,  there are 2 different points for that value since the lines are not crossing there

when x=x2, y=y3 , there is only one solution that satisifies BOTH lines at the same time.

anonymous · Answer

@amistre64 @jim_thompson5910 
Thank you both for taking the time to explain the process in detail! Now it makes a little more sense! :) Appreciate it, you two are my favorite openstudy teachers here haha :)

amistre64 · Answer

jims pretty good, ill admit that  :)

jim_thompson5910 · Answer

You're welcome. I'm glad it's making a bit more sense now.