Question

How do you solve the system `5x + 3y =3` and `x+ 9y = 2`?

Answer 1

`5x+ 3y =3`......equation`(1)`
`x+ 9y = 2`
`x=color(blue)( 2-9y` .........equation `(2)`

Solving by substitution
substituting equation `(2)` in equation `(1)`

`5x + 3y =3`
`5color(blue)((2-9y)) + 3y =3`
`10 - 45y+ 3y =3`
`-42y=-7`
`color(blue)(y)=1/6`

finding the value of `x` by substituting the value of `y` in equation `(2)`
`x= 2-9y`
`x= 2-9(1/6)`
`color(blue)(x)= (12-9)/6 = 3/6 = 1/2`

the solution for the system of equations is
`color(blue)( x = 1/2 , y =1/6`