Question

How do you solve the system of equations `10x-2y=-92` and `7x+4y=-59`?

Answer 1

`x=-9` and `y=1`

Explanation:

In the given equations

`10x-2y=-92` ...............................(1) and

`7x+4y=-59` ...............................(2),

we find that coefficients of `y` are opposite in sign and in equation (2) it is double in (1).

Hence we double the equation (1) and add it equation (2) to get

`2xx(10x-2y)+7x+4y=-2xx92-59`

or `20x-4y+7x+4y=-184-59=-243`

or `27x=-243` and

`x=-243/27=-9`

Putting this in (1), we get `10xx(-9)-2y=-92`

or `-90-2y=-92` i.e. `-2y=-92+90=-2` and `y=1`

Hence, solution is `x=-9` and `y=1`