Question

Solve the system using elimanation:
5x + 4y = 12
3x -3y = 18

Answer 1

I know how to solve a system like this using substitution but I would like to learn the elimanation method.

Answer 2

Try to even out y:
$$3(5x + 4y = 12) \implies 15x + 12y = 36$$
$$4(3x - 3y = 18) \implies 12x - 12 = 72$$

Answer 3

Do you know what to do from there?

Answer 4

@Algorithmic yes I do. I add the two systems correct?

Answer 5

Solving a system with elimination means to eliminate one variable by adding (or subtracting) the two equations.

Currently, adding or subtracting the two equations will not get us anywhere.

So, multiply the 2nd equation by 4/3.

Then we have: 5x + 4y = 12
4x - 4y = 24.

Now, we can simple add the two equations. And the result will be 9x = 36. So x = 4.

Then one can solve for y.

As you can see elimination involves a little intuition as to which equation to multiply.

Answer 6

Yes. Want me to show you or do you think you can attempt it yourself?

Answer 7

I think I can attempt it myself can you wait a second while I do the mathematics?

Answer 8

Sure. :-)

Answer 9

5x+4y=12
3x-3y=18

Find a the lowest common multiple of any one of the terms between the two equations. 5x ad 3x are both factors of 15 so I would choose that. However, because I want to cancel the x terms, I'll multiply 5x+4y=12 times 3 and 3x-3y=18 by -5 so that I get:

15x+12y=36
-15x+15y=-90

Then just combine like terms.

0x + 27y = -54
y = -2.

Then just plug in -2 into y for any of the equations.
3x - 3(-2) = 18
3x +6 = 18
3x = 12
x = 4.

Answer 10

15x + 12y = 36
+ 12x - 12y = 72
= 27x = 108
x = 4

Answer 11

Thank you Kevin, but I like trying to attempt the problems myselfs. All I needed was a little hint. :3