Find the value of m given two equations with two variables

The solution to the system of equations 5m + n = 26 and m - n = 4 is m = 5 and n = 1. Calculating m^n results in 5^1 = 5.

Answer

The problem is to solve a system of two linear equations and then calculate the value of

.
The given equations are:

We can solve this system of equations using the method of elimination.
Add equation (1) and equation (2):

Combine like terms:

Divide both sides by 6 to solve for

Now substitute the value of

into equation (2) to solve for

Subtract 5 from both sides:

Multiply both sides by -1 to solve for

Now we need to calculate

.
We have

and

To verify our solution, we can substitute

and

into equation (1):

This is correct.

Final Answer: The final answer is

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Find the value of m given two equations with two variables

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