SOLUTION: So, my problem is this I solved it once and I got it wrong can you guys help me out? 8x-6y=-2 8x+5y=-13 I am supposed to use the elimination method and get an ordered pair and

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Question 1205725: So, my problem is this I solved it once and I got it wrong can you guys help me out?
8x-6y=-2
8x+5y=-13
I am supposed to use the elimination method and get an ordered pair and I am still confused.
Found 4 solutions by math_tutor2020, ikleyn, MathLover1, MathTherapy:
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Notice the 8x terms are in common to both equations.
This will allow us to subtract the equations straight down to eliminate the x terms entirely.
The y terms subtract to -11y.
The right hand sides subtract to 11.

We end up with -11y = 11 that solves to y = -1.

Then use that y value to find x.
Let's say we plugged it into the 1st equation.
8x - 6y = -2
8x - 6(-1) = -2
8x + 6 = -2
8x = -2-6
8x = -8
x = -8/8
x = -1

Or we could pick on the 2nd equation instead.
8x+5y = -13
8x+5(-1) = -13
8x-5 = -13
8x = -13+5
8x = -8
x = -8/8
x = -1

The answer as an ordered pair is (x,y) = (-1,-1)
This is where the two lines intersect.
A graphing tool like Desmos can be used to confirm. GeoGebra is another recommended tool.

Another way to check is to plug x = -1 and y = -1 into each original equation. Then simplify.
You should get the same number on both sides.

Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.
So, my problem is this I solved it once and I got it wrong can you guys help me out?
8x-6y=-2
8x+5y=-13
I am supposed to use the elimination method and get an ordered pair and I am still confused.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

Nice problem for the Elimination method.

Simply subtract first equation from the second equation.

The terms '8x' and '8x' will cancel (will kill / will annihilate) each other,
and you will get

    5y - (-6y) = -13 - (-2)

    5y + 6y = -13 + 2

      11y   =    -11

        y   =   = -1


Thus you just found out one unknown: y = -1.


Now substitute this value  y= -1  into first equation

    8x + 5*(-1) = -13

    8x - 5 = -13

    8x = -13 + 5 

    8x = -8

     x =  = -1.


ANSWER.  x= -1,  y= -1.

Solved.



Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

.....eq.1
....eq.2
-------------------------------subtract eq.2 from eq.1 to eliminate








go to
.....eq.1, substitute










Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
So, my problem is this I solved it once and I got it wrong can you guys help me out?
8x-6y=-2
8x+5y=-13

I am supposed to use the elimination method and get an ordered pair and I am still confused.

8x - 6y = - 2 ------ eq (i)
8x + 5y = -13 ------ eq (ii)

Notice that both equations have IDENTICAL x variables. In order to ELIMINATE ths x-variable and
solve for the other variable (y, in this case), we need to either SUBTRACT eq (i) from eq (ii),
or vice-versa. I chose to do the former.

          8x - 6y = - 2 ------ eq (i)
          8x + 5y = - 13 ----- eq (ii)
              11y = - 11 ----- Subtracting eq (i) from eq (ii)
              

Now, substitute - 1 for y in either eq (i) or eq (ii). Again, I chose the former.
          8x - 6y = - 2 ------ eq (i)
      8x - 6(- 1) = - 2  ----- Substituting - 1 for y in eq (i)
           8x + 6 = - 2
               8x = - 8
              

              Finito!!
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