Question

What is the answer? Use elimination or substitution to solve `-5x+14y=17" "and" "9x-6y=27`

Answer 1

`x=5 and y=3`

Explanation:

Let the equations be:
`-5x+14y-17=0 " "`(be equation 1)
`" "9x-6y-27=0" "` (be equation 2)

(equation 1 implies)=> `14y=5x+17`

=> `" "y= (5x+17)/14` (be equation 3)

(Substitute into equation 2 )

`9x-6{(5x+17)/14}-27=0" "larr xx 14`

=> `126x-30x-102-378=0`

=> `96x-480=0`

=> `96x=480`

=> `x= 480/96`

=> `x= 5`

Now, substitute into equation 3

=> `y= {5(5)+17}/14" "`(taking x=5)

=> `y= {(25)+17}/14`

=> `y= 42/14`

`y=3`

Answer 2

`y=3,x=5`

Explanation:

`:.-5x+14y=17---------(1)`

`:.9x-6y=27-----------(2)`

`:.(1)xx9`

`:.-45x+126y=153------(3)`

`:.(2)xx5`

`:.45x-30y=135-------(4)`

`:.(3)+(4)`

`:.96y=288`

`:.y=3`

substitute `y=3` in`(2)`

`:.9x-6(3)=27`

`:.9x-18=27`

`:.9x=27+18`

`:.9x=45`

`:.x=5`

~~~~~~~~~

check:-

Substitute `y=3`and `x=5` in `(2)`

`:.9(5)-6(3)=27`

`:.45-18=27`

`:.27=27`