Question

How do you solve the system of equations `13x + 9y = 155` and `14x + 10y = 166`?

Answer 1

`(986,-1407)`

Explanation:

The first step is to solve one of the equations (it doesn't matter which one) for `y` in terms of `x`.

`14x+10y=166`

Subtract `10y` from both sides

`14x= -10y+166`

Divide both sides by 14

`x=-10/14y-166/14`

Reduce the fractions to lowest terms

`x=-5/7y-133/7`

Next, take the expression equal to `x` and plug it into the other equation.

`13color(red)(x)+9y=155`

`13(color(red)(-5/7y-133/7))+9y=155`

`-65/7y-1729/7+9y=155`

Multiply everything by `7` to get rid of all fractions

`-65y-1729+63y=1085`

Combine like terms

`-2y=2814`

Divide both sides by `-2`

`y=-1407`

Finally, plug this value for `y` back into the equation for `x`

`x=-5/7color(red)(y)-133/7`

`x=-5/7(color(red)(-1407))-19`

`x=-5(-201)-19`

`x=1005-19`

`x=986`

So the solution to both equations is `(986,-1407)`