# Thread: Solving Systems Using Elimination

1. ## Solving Systems Using Elimination

I need help solving this problem using elimination

2x-2y=61
2x+y=-7

2. 2x+2y=61 2x+y=7

2x+2y=61
-2y -2y
__________
2x = 61 - 2y
___________
2 -> divide both sides by 2

x = 30.5 - y

put this x value into other equation:

2(30.5 -y) +y = 7
61 - 2y + y = 7
-y -y
______________
61 - 2y = 7 - y
+2y +2y
______________
61 = 7 + y
-7 -7
______________
56 = y

Now substitute 56 for y:

2x + 2(56) = 61
2x + 112 = 61
-2x -61 -61 -2x
__________________
51 = -2x
________
-2 -> divide both sides by (-2)
x = -25.5

Now put (-25.5) for x and 56 for y to check your answers:

2(-25.5) + 2(56) = 61
-51 + 112 = 61
61 = 61

=]

3. Elimination means you eliminate either the x term or the y to term to leave you with just y = or x =.

As there are 2 xs in both terms, we can subtract the second term from the first to eliminate the xs.

$2x - 2y = 61$
-
$2x + y = -7$
=
$-3y = 68$
$y = -22.666...$

Now that you have y, all you need to do is solve the first equation using y as 68.

So $2x - 2 * -22.6666... = 61$
$2x = 15.3333...$
$x = 7.6666...$

Very odd answers, but that is correct. The above poster is incorrect as he mistook 2x - 2y = 61 to be 2x + 2y = 61.

4. Originally Posted by Bruce
Elimination means you eliminate either the x term or the y to term to leave you with just y = or x =.

As there are 2 xs in both terms, we can subtract the second term from the first to eliminate the xs.

$2x - 2y = 61$
-
$2x + y = -7$
=
$3y = 68$
$y = 22.666...$

Now that you have y, all you need to do is solve the first equation using y as 68.

So $2x - 2 * 22.6666... = 61$
$2x = 106.3333...$
$x = 53.1666...$

Very odd answers, but that is correct. The above poster is incorrect as he mistook 2x - 2y = 61 to be 2x + 2y = 61.
you have not conducted this properly, as you did not divide by the remaining co-efficient infront of the x...

5. I realised my mistake. I have edited my post.