# 2x + 3y = 2 and 5X - 5y = 10 solve for x and y

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2X+3y = 2

5x-5y = 10 ==> 5(x-y) = 10 ==> x-y = 2

now, y = x-2

substitute the y value in the first equation,

2x + 3 (x-2) = 2

==> 2x + 3x -6 = 2

==> 5x = 8

==> x = 8/5

then y = x-2 = 8/5 -2 = -2/5

It is easy to see that, the second equation, after factorization, will look like:

5(x-y)=10

We'll divide it by 5 and we'll get:

x-y=2

The first equation looks like:2x + 3y = 2

We'll try to reduce the unknown y, by multiplying the equation x-y=2 by 3 and, after that, we'll add it to the equation 2x + 3y = 2.

3x-3y+2x+3y=6+2

After reducing the terms 3y and -3y, we'll get:

5x=8

**x= 8/5 = 1.6**

Now, we'll find out y by substituting x into the equation:

x-y=2

1.6 - y = 2

We'll subtract 1.6 both sides:

-y = 2 - 1.6

-y = 0.4

We'll multiply both sides by (-1).

**y=-0.4**

2x+3y = 2...........(1)

5x-5y = 10..........(2)

To solve the equatons.

We can reduce the 2nd equation and rewrite: x-y = 2. Or x = y+2 and make the substitution in eq(1):

2(y+2)+3y =2. Or 2y+4+3y =2. Or 5y = -2. Or y = -2/5. Therefore x = y+2 = -2/5+2 = 8/5

5(x-y)=10 take 5 out

5(x-y)/5=10/5 divide both sides by 5

x-y= 2 or,

y=x-2..........1

substitute the value of y in 2x + 3y = 2

2x + 3(x-2) =2

2x + 3x - 6 = 2

5x = 8

x = 8/5

substitute the valueof x in equation 1

y = 8/5 - 2

y = -2/5