Question

How do I use elimination to find the solution of the system of equations `4x+3y=7` and `3x+5y=8`?

Answer 1

`4x+3y = 7` ..........equation `(1)`
`3x +5y =8` ..........equation `(2)`

multiplying equation 1 by 3 and equation 2 by 4 :

`(4x+3y = 7) xx 3`
`12x + 9y = 21`........equation `(3)`

and:

`(3x +5y =8) xx 4`
`12x +20y = 32`.......equation `(4)`

on subtracting equation `4` from `3`,
`12x` gets cancelled

`cancel12x + 9y = 21`
`-cancel12x -20y = -32`

`-11y= -11`
`y =1`

substituting this value of `y` in equation 1:

`4x+3(1) = 7`
`4x = 7-3`
`4x = 4`
`x = 1`

the solutions for the system of equations are :
`color(blue)x=1`
`color(blue)y=1`