Help with Elimination Method in Simultaneous Equations please?

Question

Please help, I have been giving some math homework to do on Elimination Method in Simultaneous Equations.
Some of the equations are:
3x - 2y=7 and 4x - 4y=8
-2x - 5y= -6 and 3x + 4y=2

How do you work them out, thanks so much =)

Answer 1

okay if you rewrite the first one
4x-4y=8
3x-2y=7 ....then you want to be able to add or subract to eliminate a variable, so multiple the entire second equation by 2, so that you can eliminate the y
4x-4y=8
6x-4y=14 ....now subtract
-2x=-6
x=3 ....now subsitute into either original
if you used to first one... 3(3)-2y=7
9-2y=7
-2y=-2
y=1..... so x=3, and y=1 or you can write (3,1)


for number 2
3(-2x-5y=-6)
2(3x+4y=2)

-6x-15y=-18
6x+8y=4...now add
7y=-14
y=-2

-2x-5(-2)=-6
-2x+10=-6
-2x=-16
x=8

(8,-2)

Answer 2

(1) 3x - 2y = 7
(2) 4x - 4y = 8
Multiply (1) through by -1 and you get:
(1) -3x + 2y = -7, then,
multiply each term in (1) by 2 and you get:
(1) -6x +4y = -14, then, put Eqn. (2) on top of Eqn. (1)
and you get:
(2) 4x - 4y = 8
(1)-6x + 4y =-14
Add them [4x +(-6x) = -2x etc.]
and y is eliminated because[( -4y) + (+4y)] equals ZERO:
-2x = -6
2x = 6
x = 3
You now know the value of x, which you may now substitute into Eqns. (1) & (2) to find the value of y to complete your solution.
Rearrange the original equations to make y (which is what you want) the subject of the equations:
(1) -2y = 7 - 3x (2) -4y = 8 - 4x.
Multiply both equations through by -1 to reverse the signs and make it easier to work with:
(1) 2y = -7+ 3x (2) 4y = -8 + 4x.
Substitute. x = 3.
(1) 2y = -7+ (3*3) (2) 4y = -8+ (4*3)
2y = 2, 4y = 4; so y = 1.
x = 3, y= 1. [Answer].

Answer 3

3x-2y = 7
4x - 4y = 8

decide which one of the variables you want to eliminate. say x.

multiply the first equation by 4 and the second by 3. That way you will have,

12x-8y = 28
12x-12y = 24

when you subtract the second equation from the first one, you will get,

4y = 4
y = 1

Now substitute 1 for y in either of the original equations and solve for x. x = 3.

Use the same concept for the second one.