We have to find m and n using the equations :

mx - y = 23...(1)

nx + y = 12...(2)

Now we see that there are 4 terms m, n, x and y in the two equations given. So we can only write 2 of them in terms of the others.

Using (1), we can write, m in terms of x and y as

mx - y = 23

=> m = (23 + y) / x

Using (2), we can write n in terms of x and y as

nx + y = 12

=> n = (12 - y) / x

**Therefore m and n in terms of x and y are m=(23 + y)/x and n=(12 - y)/x**

mx - y = 23.............(1)

nx + y = 12............(2)

Let us add (1) and (2):

==> nx + mx = 35

==> (n+m) x = 35

==> n + m = 35/ x

==> n = 35/x - m

But : mx - y = 23

==> m = (y+ 23)/x

**==> n = 35/x - (y+23)/ x**

=> m = 35/x - n

But : nx + y = 12

==> n = 12-y)/ x

**==> m = (35/x) - (12-y)/x**

mx - y = 23

mx = y + 23

`m = (y + 23)/x`

The second one :

nx + y= 12

nx = 12 - y

` n = (12 - y)/x `

mx-y=23

the first step is to add y

mx = 23 + y

divide by x because were are trying to solve for m

`x = 23/x + y/x ` this can also be written as `x = (23 + y) / x`

nx+y=12

subtract y

nx = 12 - y

divide by x

`n = 12/x - y/x` which can also be written as `n=(12-y)/x`

mx-y=23

nx+y=12

To solve for a variable in terms of another variable means to isolate the variable you want from the rest.

Lets deal with the first one :

mx - y = 23

mx = y + 23

m = (y + 23)/x

Now the second one :

nx + y= 12

nx = 12 - y

n = (12 - y)/x

To solve for m and n in equations:

mx-y=23...(1).

nx+y=12...(2).

We can treat both the graphs as independent, as there are no relationship given between the graphs at (1) and (2).

Both equations represent different straight lines.

From the first equation, mx-y = 23,

mx = 23+y

m = (23+y)/x is the solution for m.

From the 2nd equation nx+y = 12. we get:

nx = 12-y

n = (12-y)/x.

Therefore the solution for n and m are m = (23+y)/x and n = (12-y)/x.