Question

How do you solve the following system?: `2x + 3y = 1 , -3x + 7y = 1`

Answer 1

Solution: `x = 4/23 , y =5/23`

Explanation:

`2 x + 3 y =1 ; (1) , -3 x +7 y =1 ; (2)` Multiplying equation

(1) by `3` and equation (2) by `2` we get,

`6 x + 9 y =3 ; (3) , -6 x +14 y =2 ; (4)` Adding equation

(3) and equation (4) we get, `23 y= 5 :. y =5/23`. Putting

`y =5/23` in equation (1) we get, `2 x +3*5/23=1` or

`2 x=1-15/23 or 2 x = (23-15)/23 or 2 x =8/23 or x = 4/23`

Solution: `x = 4/23 , y =5/23`[Ans]

Answer 2

`y=5/23`

`x=4/23`

Explanation:

`2x+3y=1`
`-3x+7y=1`

Probably the easiest way to solve this is by elimination; notice there is a GCD of `2x` and `-3x` of `6x` so let's multiply both equations by 3 and 2 respectively:

`3(2x+3y=1)`
`2(-3x+7y=1)`

`6x+9y=3`
`-6x+14y=2`

now add the equations together, notice the x terms are eliminated:

`23y=5`

`y=5/23`

now use either original equations with the y value you found to solve for x:

`2x+3(5/23)=1`

`x=4/23`