Question

How do you solve `3x + 7y = 18` and `x + 2y = 5`?

Answer 1

The solution for the system of equations is:

`color(green)(x=-1`

`color(green)(y = 3`

Explanation:

`3x + 7y = 18`........equation `(1)`

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

Substituting equation `2` in equation `1:`

`3x + 7y = 18`

`3 xx (color(blue)( 5 - 2y)) + 7y = 18`

`15 - 6y + 7y = 18`

`15 + y = 18`

`y = 18 - 15`

`color(green)(y = 3`

Now we substitute the value of `y` in equation `2` to find `x:`

`color(blue)(x = 5 - 2y`

`x = 5 - 2 xx (3)`

`x = 5 - 6`

`color(green)(x=-1`