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

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

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)

jess1999 | Student, Grade 9 | (Level 1) Valedictorian

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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

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

2y = 2 now divide both sides by 2

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

pinkcheez95 | Student, Grade 10 | eNotes Newbie

Posted on

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