# How to use method of elimination for? How can i figure this out? 4x - 9y = 4...

How to use method of elimination for?

How can i figure this out? 4x - 9y = 4

6x +15y = -13

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You want to reduce the system of two equations in two unknowns to one equation with one unknown. You can either eliminate `x` or ` ``y` , so choose whichever looks easiest. Here, it's easiest to eliminate `x`. The basic idea is to get the coefficients to be negatives of one another.

To do this, multiply the top equation by 3 and the bottom equation by -2. This gives the new system

`12x-27y=12`

`-12x-30y=26.`

Now if we add the two vertically, the `x` terms will cancel and we get

`-57y=38` , so `y=-38/57=-2/3.`

Now we can plug this value of `y` back into either of the original equations to solve for `x`. It looks like the first equation will be easiest:

`4x-9(-2/3)=4=>4x+6=4=>4x=-2=>x=-1/2` .

**The solution is `x=-1/2`, `y=-2/3` , and you should check that these values make both of the original equations true.**