It might benefit you to learn about the quadratic equation as well. It is (-b +- √b^2 - 4ac)/(2a). It is commonly used to solve quadratic equations of form ax^2 + bx + c. There are also many other ways to solve, such as completing the square. I'd recommend learning about them, they are very interesting!
First, we add the first and third equations to get -x+3z=8. Then, we multiply the first equation by two and add the third equation to that to get 3y+5z=9. Then, we subtract that from the second equation to get -3x-2y=1. Then, we add the first equation to the second and subtract the third equation from that to get 7y+6z=4. This means that we now have the equations
Looking at the second and fourth equations, we find that y = -2 and that z = 3. Solving for x, we find that x = 1. I'll leave the checking up to you.