Question

How to solve the system of equation 500y-600x=2800 , 400y-400x=2400 by elimination

Please help me solve this, I have about 3 hours and I dont understand how to solve this

Answer 1

`x=2` and
`y=8`

Explanation:

Given:

Equation 1:

`500y-600x=2800`

Simplifying the above equation by dividing both sides by 100

`(500y-600x)/(100)=(2800)/(100)`

`(500y)/(100)-(600x)/(100)=28\\\\5y-6x=28`

Equation 2:

`400y-400x=2400`

Simplifying the above equation by dividing both sides by 400.

`(400y-400x)/(400)=(2400)/(400)`

`(400y)/(400)-(400x)/(400)=6\\\\y-x=6`

Now the system of equation is:

(1a)
`5y-6x=28`

(2a)
`y-x=6`

Solving by elimination

Multiplying equation (2a) with
`-5`

`-5(y-x)=-5* 6`

(2b)
`-5y+5x=-30`

Adding equations (1a) and (2b) in order to eliminate
`y`

`5y-6x=28`

+
`-5y+5x=-30`

We get
`-x=-2`

∴
`x=2`

Plugging
`x=2` in equation (2a).

`y-2=6`

Adding
`2` both sides.

`y-2+2=6+2`

∴
`y=8`