Question

How do you solve `5x+y=1` and `3x+2y=2` using substitution?

Answer 1

`color(green)(x = 0, y = 1`

Explanation:

`5x + y = 1` Eqn (1)

`y = 1 - 5x`

`3x + 2y = 2` Eqn (2)

Substituting value of y in second equation in terms of x,

`3x + (2* (1-5x) = 2`

`3x + 2 - 10x = 2`

`-7x = 2 - 2 = 0` or `x = 0`

Substituting value of x in Equation (1),

`(5*0) + y = 1` or `y = 1`

Solution `color(green)(x = 0, y = 1)`

Answer 2

`x=0`
`y=1`

Explanation:

Given -

`5x+y=1` ---------------(1)
`3x+2y=2` ---------------(2)

`5x+y=1` ---------------(1)`xx2`
`10x+2y=2` ------(3)
`3x+2y=2` -------(2) `(3) - (2)`
`7x=0`
`x=0/7=0`

Substitute `x=0` in equation (1)

`5(0)+y=1`
`y=1`