How do I solve for m and n? mx-y=23 nx+y=12

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

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

 

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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

givingiswinning's profile pic

givingiswinning | Student, Grade 10 | (Level 1) Valedictorian

Posted on

mx - y = 23

mx = y + 23

`m = (y + 23)/x`

The second one : 

nx + y= 12

nx = 12 - y

` n = (12 - y)/x `

 
 
atyourservice's profile pic

atyourservice | Student, Grade 11 | (Level 3) Valedictorian

Posted on

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`

Wiggin42's profile pic

Wiggin42 | Student, Undergraduate | (Level 2) Valedictorian

Posted on

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

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

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.

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