Ellason wants to solve the following system using the elimination method:

5x + 2y = 30
x + y = 8

what number should the equation x + y = 8 be multiplied by to eliminate y?

Solutions 

1) Multiply the 2nd row by 5

5x+2y=30

5x+5y=40 

2) Subtract the 2nd row from the 1st row

−3y=−10 

3) Solve for the variable y in the above equation

⇒ Solve for y

−3y=−10 

⇒ Divide both sides by −3

y=−10 / −3

⇒ Simplify 10 / −3 to −10 / 3

y=10 / 3 

4) Substitute y=10 / 3 into any of the two equations above.Let's pick the first equation 5x+2y=30. 

5x+2× 10 / 3 = 30 

5) Solve for x in the above equation  

(there are more steps but the answer is below) 

x=14 / 3 

Therefore,

x=14 / 3 

y=10 / 3

5x + 2y = 30
x + y = 8

when multiplying an equation every term is multiplied
eg:
x + y = 8 //multiply by 3
3*x + 3*y = 3*8
3x + 3y = 24

in elimination method two equations are added when there are oposite coefficients of chosen variable

5x + 2y = 30 coefficient of y is 2
x + y = 8 //multiply by -2

5x + 2y = 30
-2x - 2y = -16
sum
5x-2x+2y-2y=30-16
3x = 14  //y has been eliminated (elimination method)

the number is -2