System of Equations

<a href="https://www.prepswift.com/quizzes/quiz/prepswift-system-of-equations" target="_blank">System of Equations Exercise</a> Note: towards the end of the video, Greg notes that the system of equations is "unsolvable". This isn't quite right, as the two equations essentially reduce to one. As a result, you can have infinite values of x and y that satisfy the equation, which means that the system of equations actually have infinite solutions.  To make the system of equation unsolvable, simply change the RHS of either equation. So the system -2x + 3y = 12 and -6x + 9y = 33 is unsolvable, because if we multiply the first equation by 3, we get -6x + 9y = 36, which implies that 36 = 33, which is not possible. When you have two more equations, each containing two or more variables, you have Systems of Equations. <ul> <li>Example 1 (a set of two equations, each with two variables)</li> </ul> $$3x-5y=28$$ $$7x+10y=-5$$ <ul> <li>Example 2 (a set of three equations, each with three variables)</li> </ul> $$3x-5y+4z=28$$ $$7x+10y-z=-5$$ $$-4x+y+z=19$$ NOTE: Systems of equations are solvable if the number of variables in each equation equals the number of equations in the set. For example, to solve a system of four equations, each equation would need to contain the four variables in question.