Simultaneous equation help?

Question

2x - 3y = 8
3x + 4y = -22

Answer 1

[2x-3y=8]*4
[3x+4y=-22]*3
8x-12y=32
9x+12y=-66 add
17x=-34
x= -2
y= -4

Answer 2

2x - 3y = 8
3x + 4y = -22

multiply top line by 4 and bottom line by 3

8x - 12y = 32
9x + 12y = -66

cancel the 2 12y's

8x = 32
9x = -66

then add 8x and 9x and take 32 from the -66

17x=-34

x = 2

sub 2 back into original line for x

3x + 4y = -22
3(2)+4y=-22
6+4y=22

bring 6 accross and change the sign infront of it

4y=22-6
4y=16
y=4

Answer 3

2x - 3y = 8
3x + 4y = -22

multiply top line by 4 and bottom line by 3

8x - 12y = 32
9x + 12y = -66

cancel the 2 12y's

8x = 32
9x = -66

then add 8x and 9x and take 32 from the -66

17x=-34

x = 2

sub 2 back into original line for x

3x + 4y = -22
3(2)+4y=-22
6+4y=22

bring 6 accross and change the sign infront of it

4y=22-6
4y=16
y=4

Answer 4

A few easy ways to solve simultaneous equations. One is to solve one equation in terms of one of the variables and replace it into the second equation:
2x-3y = 8
2x=8+3y
x= 4 +3/2 y
Then replace this into equation 2.
3(4+3/2 y) + 4 y =-22
12 + 9/2y + 4 y = -22
12 + 9/2 y + 8/2 y = -22
17/2 y = -34
y = - 4
Place back into your first solved equation
x = 4 + 3/2 x (-4) = -2

Another easy way is to manipulate one equation and add them so you eliminate one of your variables:
2x- 3y = 8 (want -4y so when you add the y's cancel so multiply both sides by 4/3)
8/3 x - 4 y = 32/3
Now add your two equations
8/3 x + 3x + 4y - 4y = 32/3 - 22
17/3 x = -34/3
x=-2
Putting back in the first equation you get y = -4

At a more advanced level you can approach it in matrix form. We can rewrite the equations:
[ 2 -3; 3 4] [x; y] = [8; -22]
Then multiply both sides by the inverse of [2 -3; 3 4] which you can calculate by hand or get from a calculator or matlab as [..2353 .1765; -.1765 .1176] .
Multiplying both sides by this we again end up with
[x; y] = [-2;-4]

Answer 5

2x - 3y = 8
3x + 4y = -22

Multiply first equation by 3:
3(2x - 3y) = 3*8
6x - 9y = 24

Multiply second equation by 2:
2(3x + 4y) = 2(-22)
6x + 8y = -44

Subtract "new" first from "new" second
(6x + 8y) - (6x - 9y) = -44 - 24
17 y = -68
y = -68 / 17
y = -4

Subsitute y = - 4 in 2x - 3y = 8
2x - 3(-4) = 8
2x + 12 = 8
2x = -4

x = -2
y = -4

CHECK:
2x - 3y = 2(-2) - 3(-4) = -4 + 12 = 8
3x + 4y = 3(-2) + 4(-4) = -6 - 16 = -22

Answer 6

x the top one by 3
and the other 1 by 2
6x - 9y = 24
6x+ 8y = -44 now take top 1 away
17y = -68 y = -4
2x -12 = 8
2x = 20 x = 10

Answer 7

This website page explains how to do these in very easy terms. Have a look. You'll feel much better when you can work them out for yourself.

http://www.bbc.co.uk/schools/gcsebitesize/maths/algebraih/simultaneousrev2.shtml

Answer 8

8x - 12y = 32
9x + 12y = - 66------ADD
17x = - 34
x = - 2

- 6 + 4y = - 22
4y = - 16
y = - 4

x = - 2 , y = - 4