Question

How do you solve this system of equations: `3x + 6y = 105; 14x + 12y = 314`?

Answer 1

`x=13; y =11`

Explanation:

`3x+6y=105;14x+12y=314`

dividing the entire `2^(nd)` equation by 2, the two equations now are,
`3x+6y=105` and `7x+6y=157`

subtracting the `1^(st)` equation from the `2^(nd)`,
`4x=52`
`x=13`

now, substitue the `x` in (any equation, here im going for) the `1^(st)` one.

`3(13)+6y=105`
`6y=105-39`
`6y=66`
`y=11`.

-Sahar

Answer 2

`color(green)(x = 13, color(blue)(y=11)`

Explanation:

`3x + 6y = 105` Eqn(A)

`14x + 12y = 314` Eqn (B)

(B) - 2(A) gives

`14x - 6x + 12y - 12y = 314 - 210`

`8x = 104, or x = 13`

Substituting value of x in Eqn (A)

`(3*13) + 6y = 105`

`6y = 105-39 = 66, y = 66/6 = 11`