Question

3x + 4y = 7, 8x + 5y = 12. The value of x and y is

13, 20
20, 13
13/17, 20/17
20/17, 13/17

Answer 1

13/17, 20/17

Explanation:

3x + 4y = 7 --- Equation 1

Equation 1×5:

15x + 20y = 35 --- Equation 2

------------------------------------------------------------------------------------------------------------

8x + 5y = 12 --- Equation 3

Equation 3×4:

32x + 20y = 48 --- Equation 4

------------------------------------------------------------------------------------------------------------

Equations 4-2:

32x + 20y - 15x - 20y = 48 - 35

17x = 13

x =
`(13)/(17)`

Substitute x =
`(13)/(17)` into Equation 1:

3x + 4y = 7

3(
`(13)/(17)`) + 4y = 7

`(39)/(17)` + 4y = 7

4y = 7 -
`(39)/(17)`

=
`(119)/(17)` -
`(39)/(17)`

=
`(80)/(17)`

y =
`(80)/(17)` ÷ 4

y =
`(20)/(17)`

Thus, x =
`(13)/(17)`, y =
`(20)/(17)`.

(
`(13)/(17)`,
`(20)/(17)`)