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) About Me  (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

1%2Ax-4%2Ay=-19
-1%2Ax%2B6%2Ay=27

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:

-1%2A%281%2Ax-4%2Ay%29=%28-19%29%2A-1 Multiply the top equation (both sides) by -1
-1%2A%28-1%2Ax%2B6%2Ay%29=%2827%29%2A-1 Multiply the bottom equation (both sides) by -1


So after multiplying we get this:
-1%2Ax%2B4%2Ay=19
1%2Ax-6%2Ay=-27

Notice how -1 and 1 add to zero (ie -1%2B1=0)


Now add the equations together. In order to add 2 equations, group like terms and combine them
%28-1%2Ax%2B1%2Ax%29%2B%284%2Ay-6%2Ay%29=19-27

%28-1%2B1%29%2Ax%2B%284-6%29y=19-27

cross%28-1%2B1%29%2Ax%2B%284-6%29%2Ay=19-27 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:

-2%2Ay=-8

y=-8%2F-2 Divide both sides by -2 to solve for y



y=4 Reduce


Now plug this answer into the top equation 1%2Ax-4%2Ay=-19 to solve for x

1%2Ax-4%284%29=-19 Plug in y=4


1%2Ax-16=-19 Multiply



1%2Ax=-19%2B16 Subtract -16 from both sides

1%2Ax=-3 Combine the terms on the right side

cross%28%281%2F1%29%281%29%29%2Ax=%28-3%29%281%2F1%29 Multiply both sides by 1%2F1. This will cancel out 1 on the left side.


x=-3 Multiply the terms on the right side


So our answer is

x=-3, y=4

which also looks like

(-3, 4)

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

1%2Ax-4%2Ay=-19
-1%2Ax%2B6%2Ay=27

we get



graph of 1%2Ax-4%2Ay=-19 (red) -1%2Ax%2B6%2Ay=27 (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 (-3,4). This verifies our answer.

Answer by MathTherapy(10552) About Me  (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 = 8%2F2, or highlight_green%284%29



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

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

      x  = - 19 + 16

      x  = highlight_green%28-+3%29

That's all!! It is that simple!