In AP Calculus, we aren't often called upon to solve systems of equations, which means that when it happens we are usually "rusty" on using Kramer's Rule, Gaussian Elimination, and other techniques. On the TI89, you can use the solve() command (among other methods) to solve systems of linear equations  when you need it, it can be a real timesaver!
"Normal" syntax for solve() is:
solve(equation, variable)
To use solve() to solve a system of linear equations, you separate each equation with "and", and enclose a commaseparated list of variables by curly brackets "{}".
solve(equation 1 and equation 2 and equation 3 ... , {variable 1, variable2, variable3, ...})
Here are a couple of examples:
To solve the system: x + 2y = 3 Type: solve( x+2y=3 and 2xy=1,{x,y}) Note:


For a more "interesting" example, consider problem 51 on page 249 of the Stewart text (Section 4.3)" "Find a cubic equation f(x) = ax3 + bx2 + cx + d that has a local maximum value of 3 at 2 and a local minimum of 0 at 1." A straightforward solution of this problem leads to a system of 4 equations with 4 unknowns: a + b + c + d = 0 This system can be solved using: solve(a + b + c + d = 0 and 8a + 4b  2c + d = 3 and 12a  4b + c = 0 and 3a + 2b + c = 0, {a,b,c,d}) Giving: a = 2/9, b = 1/3, c = 4/3, and d = 7/9 
