Please solve this with elimination

Question

x/2 + y/5 = 13/10 

 

3(x-y) = x-10

Answer 1

Same as others - get rid of fractions

 

10 * top

 

And Distribute on the bottom

 

5x + 2y = 13

3x - 3y = x - 10

 

Need all x's on the left, so subtract x from both sides of the bottom equation

 

5x + 2y = 13

2x - 3y = -10

 

 

Because the y-terms or opposite signs, this (y) is the variable we will eliminate.

 

TOP * 3

BOTTOM * 2

 

15x + 6y = 39

 4x - 6y = -20

 

Add vertically and the (6y) and (-6y) go away (are ELIMINATED).  And we are left with

 

19x = 19

 

so x = 1.

 

Plug this back in to find y.

 

4(1) - 6y = -20

 

subtract 4 from both sides.

 

-6y = - 24

 

divide both sides by  -6

 

y = 4

 

Check to be sure these answers work in BOTH original equations.