Final answer:
To solve the system of equations, you can use either substitution or elimination methods. Common practice is to solve one equation for one variable and substitute it into the other, or manipulate the equations to eliminate one variable.
Step-by-step explanation:
The solution to the system of equations 2x - 5y = 14 and x + \(\frac{3}{2}y\) = 5 can be found by using either substitution or elimination method. To use the substitution method, solve one equation for one variable and then substitute that expression into the other equation. For the elimination method, you make the coefficients of one of the variables the same and then add or subtract the equations to eliminate that variable.
In this case, it might be easier to use substitution because the second equation can be quickly solved for x, giving us x = 5 - \(\frac{3}{2}y\). We can then substitute this expression for x into the first equation and solve for y. Once we have the value of y, we can substitute it back into either original equation to find the value of x.