# How to solve this Linear system equation by using elimination method: x + 2y = 2 3x + 5y = 4

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To use this method, you have to get it so that one of your variables will cancel when you add the two equations. The best way to do that with these two equations is to make the x in the first equation be -3x. You do that by multiplying it by -3.

So now you have

-3x - 6y = -6

You add that to the other equation and you get

-y = -2 or y = 2.

Then you can just plug that in to the first equation as it originally was and you get

x + 2(2) = 2

x + 4 = 2

x = -2

You can also eliminate the variable y. In order to do so, you'll have to multiply the first equation with (-5) and the second equation with 2. Then you'll have to add the equations.

Let's see how it happens:

(x + 2y)*(-5) = 2*(-5)

(3x + 5y)*2 = 4*2

The equations will be:

-5x - 10y = -10

6x + 10y = 8

Now, we'll add the equations:

-5x + 6x - 10y + 10y = -10+8

**x = -2**

Now. we'll substitute the known value for x, into the first or the second equation. Because the form of the first equation is much simpler, we'll chhose to substitute x in the first one.

-2 + 2y = 2

2y = 4

**y = 2**

We can go for a substitution method. From the first equation , we get x=2-2y. Substitute 2-2y for x in the second equation:3(2-2y)+5y=4 . This reduces the equation to one variable in y: 6-6y+5y=4. Or 6-y =4. Or 6-4=y. So y=2.

Substituting y=2 in the first equation, x+2*2 = 2.Or x=2-4. Or x=-2.