Answer: (x, y) = (5/4, 2).
The given system of equations is:
4x - y = 3
3x + y = 4
We can solve for x and y using either substitution or elimination method.
By substitution, we can solve for y in one of the equations and substitute that value into the other equation to solve for x.
Starting with 4x - y = 3, we can add y to both sides to isolate x:
4x = 3 + y
Then, we can substitute this expression for y into the second equation:
3x + (3 + y) = 4
Expanding the right side, we get:
3x + 3 + y = 4
3x + 3 = 4 - y
3x = 1 - y
x = (1 - y)/3
Now, we can substitute the expression for x into the first equation:
4((1 - y)/3) - y = 3
4(1 - y)/3 = 3 + y
4 - 4y/3 = 3 + y
1 - 4y/3 = y + 3
-3y/3 = -2
y = 2
Finally, we can substitute the value of y into one of the original equations to find x:
4x - 2 = 3
4x = 5
x = 5/4
So, the solution to the system of equations is (x, y) = (5/4, 2).