Question

How do you solve the system `2x-y= 7` and `3x-4y= -7`?

Answer 1

`x = 7 and y = 7`

Explanation:

`2x - y = 7 - - - eqn1`

`3x - 4y = -7 - - - eqn2`

Multiply `eqn1` by `3` and `eqn2` by `2`

`3 (2x - y = 7)`

`2 (3x - 4y = -7)`

`6x - 3y = 21 - - - eqn3`

`6x - 8y = -14 - - - eqn4`

Subtracting `eqn4` from `eqn3`

`(6x - 6x) + (-3y - (-8y)) = 21 - (-14))`

`0 - 3y + 8y = 21 + 14`

`5y = 35`

`y = 35/5`

`y = 7`

Substiting the value of `y` into `eqn1`

`2x - y = 7 - - - eqn1`

`2x - 7 = 7`

`2x = 7 + 7`

`2x = 14`

`x = 14/2`

`x = 7`

Therefore;

`x = 7 and y = 7`