Question

How do you solve the system of equations `7x+5y=9` and `4x-3y=11` by elimination?

Answer 1

`x=2` and `y=-1`

Explanation:

We are given

`7x+5y=9` ...............(1) and

`4x-3y=11` ...............(2)

Here we have all coefficients different and there is no common factor between coefficients of `x` as well as between coefficients of `y`.

Hence, to eliminate, say `x`, we have to multiply (1) by the coefficient of `x` in (2) (i.e. by `4`) and to multiply (2) by the coefficient of `x` in (1) (i.e. by `7`). This makes the equations as

`28x+20y=36` ...............(3) and

`28x-21y=77` ...............(4)

Now subtracting (4) from (3) (as coefficients of `x` are both of same sign), we get

`20y-(-21y)=36-77` or `41y=-41` and `y=-1`

Now putting this in (1), we get `7x+5xx(-1)=9`

or `7x-5=9` or `7x=9+5=14` i.e. `x=14/7=2`

Hence, `x=2` and `y=-1`.