5m+n=34

m-2n=9

5m+n=34

n = 34 - 5m

m-2n=9
m - 2(34-5m) = 9
m - 68 + 10m = 9
11m = 9 + 68
llm = 77
m = 7

Now solve for n in the first equation.

so would N=1?

Right.

To find the values of variables 'm' and 'n', we can use a method called "elimination". Here's how you can solve these equations step by step:

Step 1: Multiply one of the equations by a suitable number to make the coefficients of either 'm' or 'n' the same (or opposite).

Let's multiply the second equation by 5, so it becomes:
5(m-2n) = 5(9)
This simplifies to:
5m - 10n = 45

Now we have two equations:
5m + n = 34 ...(Equation 1)
5m - 10n = 45 ...(Equation 2)

Step 2: Subtract the equations from each other to eliminate one variable.

Subtract Equation 2 from Equation 1:
(5m + n) - (5m - 10n) = 34 - 45

When we simplify this equation, the '5m' terms cancel out:
n + 10n = -11

This can be further simplified:
11n = -11

Step 3: Solve for the remaining variable.

Divide both sides of the equation by 11:
n = -11/11

This simplifies to:
n = -1

Step 4: Substitute the value of 'n' back into one of the original equations to find the value of 'm'.

Let's use Equation 1:
5m + (-1) = 34

Simplify:
5m - 1 = 34

Add 1 to both sides of the equation:
5m = 35

Divide both sides of the equation by 5:
m = 35/5

This simplifies to:
m = 7

So, the values of 'm' and 'n' that satisfy both equations are:
m = 7
n = -1