SOLUTION: This is solving systems using elimination and idk how to figure this promblem out its x-4y=-19 -x+6y=27

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Question 1008517: This is solving systems using elimination and idk how to figure this promblem out its
x-4y=-19
-x+6y=27
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

Solved by pluggable solver: Solving a System of Linear Equations by Elimination/Addition


Lets start with the given system of linear equations




In order to solve for one variable, we must eliminate the other variable. So if we wanted to solve for y, we would have to eliminate x (or vice versa).

So lets eliminate x. In order to do that, we need to have both x coefficients that are equal but have opposite signs (for instance 2 and -2 are equal but have opposite signs). This way they will add to zero.

So to make the x coefficients equal but opposite, we need to multiply both x coefficients by some number to get them to an equal number. So if we wanted to get 1 and -1 to some equal number, we could try to get them to the LCM.

Since the LCM of 1 and -1 is -1, we need to multiply both sides of the top equation by -1 and multiply both sides of the bottom equation by -1 like this:

Multiply the top equation (both sides) by -1
Multiply the bottom equation (both sides) by -1


So after multiplying we get this:



Notice how -1 and 1 add to zero (ie )


Now add the equations together. In order to add 2 equations, group like terms and combine them




Notice the x coefficients add to zero and cancel out. This means we've eliminated x altogether.



So after adding and canceling out the x terms we're left with:



Divide both sides by to solve for y



Reduce


Now plug this answer into the top equation to solve for x

Plug in


Multiply



Subtract from both sides

Combine the terms on the right side

Multiply both sides by . This will cancel out on the left side.


Multiply the terms on the right side


So our answer is

,

which also looks like

(, )

Notice if we graph the equations (if you need help with graphing, check out this solver)




we get



graph of (red) (green) (hint: you may have to solve for y to graph these) and the intersection of the lines (blue circle).


and we can see that the two equations intersect at (,). This verifies our answer.
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
This is solving systems using elimination and idk how to figure this promblem out its
x-4y=-19
-x+6y=27
Elimination, as the name implies, involves the elimination of one variable in order to find the value of the other variable

We don't have to change any of the 2 equations since the x in the 1st equation and the x in the 2nd equation have the same,

but opposite-signed coefficients

Therefore, all that's needed is the ADDITION of the 2 equations to eliminate x

  x - 4y = - 19 ------- eq (i)

- x + 6y =   27 ------- eq (ii) 

      2y =    8 ------- Adding eqs (ii) & (i)

       y = , or 



x - 4(4) = - 19 ------ Substituting 4 for y in eq (i)

x - 16   = - 19 ------ Adding 16 from both sides

      x  = - 19 + 16

      x  = 

That's all!! It is that simple! 

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