Question

How do solve the following linear system?: `5x-y=3 , x+2y=5`?

Answer 1

`x= 1, y = 2`

Explanation:

`5x - y = 3,` Eqn (1)

`x + 2y = 5` Eqn (2)

`10x - 2y = 6` Eqn (1) * 2= Eqn (3)

Add Eqns (2) & (3),

`x + 10x + cancel(2y) - cancel(2y) = 5 + 6`

`11x = 11` or `x = 1`

Substituting value of x in Eqn (1),

`5 - y = 3`

`y = 2`

Answer 2

Let's solve for `y`

`1^(st) " equation "`

`5x-y=3`

`-y=3-5x`

Multiply both sides by `-1`

`color(magenta)(y=5x-3`

Now to the second equation

`x+2y=5`

Put `y's` value

`x + (2xx(5x-3))=5`

Notice that the brackets change everything

Solve

`x+10x-6=5`

`11x-6=5`

`11x=11`

`color(red)(x=1`

Now....

`y=5x-3`

Put `x's` value

`y = 5xx1-3`

`y=5-3`

`color(red)(y=2`