I need this solved using the elimination method: 8x - 5y = -10 -2x + 5y = -20 Th

Question

I need this solved using the elimination method:                     8x - 5y = -10                     -2x + 5y = -20 The possible answers are:   A. (5,-6)                                           B.(6, -5)                                           C.(-5,-6)                                          D. (-5,-6)   I need this solved using the elimination method:                     8x - 5y = -10                     -2x + 5y = -20 The possible answers are:   A. (5,-6)                                           B.(6, -5)                                           C.(-5,-6)                                          D. (-5,-6)  

Explanation / Answer

                     8x - 5y = -10                     -2x + 5y = -20
                     6x + 0 = -30
                   
So you have the equation 6x = -30. Now solve for x:
                    6x/6 = -30/6
                         x = -5

Now that you have determined the x variable, you can now go backand plug it into any of the original equations and solve for y:
                   -2x + 5y = -20
                   -2(-5) + 5y = -20
                   10 + 5y =-20   then subtract 10 from bothsides
                         5y = -30
                          y = -6

Thus x = -5 and y = -6 and the solution to the system of equationsis (-5,-6).



Just for reference:
2)In other cases the similar terms may be exactly the same such as7x and 7x and to eliminate the x variable you would subtract thetwo equations or in other words, multiply one equation by -1 andadd them.

Ex.   3x - 2y = 5
      -( x - 2y) =-( 4)

        3x - 2y = 5
        -x + 2y = -4
        2x + 0 = 1

3)In the case where the similar terms are multiples of each othersuch as 3z and 18z, you need to first multiply the equations by anumber to get them to either of the first two cases.

Ex. 7x + 2y = 1
       21x + 5y = 4
      We can see that 7x and 21x aremultiples of each other and can fit into the first two cases if wemultiple the first equation by 3:
       3(7x+2y)= 3(1)
        21x + 6y = 3

And we use this modified equation with the second equation
        21x + 6x =3
        21x + 5x =3
With the similar terms being exactly the same as in case 2,we subtract the two equations to eliminate the x variable.


NOTE:

I should also add that if elimination does not seem possible i.e.with 2x+3y=3 and 7x+5y=1, then substitution method is the way togo.

Be aware that not all systems of equations have solutions:

2x+3y=3
4x+6y=7

We see that if we multiply the first equation by 2, we can getsimilar terms and case 2 applies.
4x+6y=6
-4x-6y=-7
0+0 = -1 ?
0 does not equal -1
0=/=-1

Since the result can never be true, there is no point ofintersection between the graphs of these two lines. Thisoccurs for parallel lines.

There also cases where you can have infinitely manysolutions. This occurs when the two equations represent thesame line i.e.   3x+2y=4
            6x+4y=8

If you multiply the first equation by 2, you end up with anequation that is identical to the second and thus and combinationof x and y will suffice provided that they exist on the graph.

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.