3x + y = 7; 2x - y = 7

To solve this system of equations, we can use the method of elimination.

First, let's add the two equations together to eliminate the y-term:

(3x + y) + (2x - y) = 7 + 7

Simplifying, we have:

3x + 2x = 14

Combining like terms, we get:

5x = 14

Dividing both sides by 5, we find:

x = 14/5

Now, substitute the value of x into one of the original equations (let's use the first one):

3(14/5) + y = 7

Simplifying, we have:

42/5 + y = 7

Subtracting 42/5 from both sides, we get:

y = 7 - 42/5

To simplify the expression on the right hand side, we need a common denominator:

y = 35/5 - 42/5

y = (35-42)/5

y = -7/5

So, the solution to the system of equations is:

x = 14/5 y = -7/5