# Find the solutions for the following system of equations. 5x + 3y = 18 and 2y -2x = -4 and explain

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Given the system:

5x + 3y = 18 ...........(1)

2y - 2x = -4

We will divide by 2:

==> y - x = -2 .............(2)

Now we will use the substitution method to solve for x and y.

First, we will rewrite equation (2).

==> y = x - 2

Now we will substitute y= x -2 into equation (1).

==> 5x + 3y = 18

==> 5x + 3(x-2) = 18

==> 5x + 3x - 6 = 18

==> 8x = 24

==> x = 24/8 = 3

**==> x= 3**

Now we to find y, we will substitute into y= x-2

==> y= x- 2 = 3 - 2 = 1

==>** y= 1**

**Then, the solution for the system is the pair ( 3, 1)**

5x + 3y = 18

2y - 2x = -4

First, switch the 2y with the -2x in the second equation. Then, multiply everything in the first equation by 2, and everything in the second equation by 3

By doing that, your equation should look like

**10x + 6y = 36**

**-6x + 6y = -12 **now subtract 6y with -6y ( which means subtract 10x with -6x and and 36 with -12 )

By subtracting, your equation should look like

**-16x = -48 **now divide both sides by -16

By dividing, your equation should look like

**x = 3 **which is your answer for " x "

Now plug 3 into one of the equation

**2y - 2 ( 3 ) = -4 **multiply -2 with 3

By multiplying, your equation should look like

**2y - 6 = -4 **now add 6 on both sides

By adding, your equation should look like

**2y = 2 **now divide both sides by 2

By dividing both sides by 2, your equation should look like

**y = 1 **which is your answer for " y "

So your answer is **x = 3 ; y = 1**

2(5x+3y=18)

5(-2x+2y=-4)

10x+6y=36

-10x+10y=-20

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16y=4

y=.25

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5x+3y=18

5x+3(.25)=18

5x+.75=18

-.75 -.75

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5x=17.25

x=3.45