<p><a href="https://www.prepswift.com/quizzes/quiz/prepswift-system-of-equations" target="_blank">System of Equations Exercise</a></p>
<p><strong>Note</strong>: 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. </p>
<p>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. </p><p>When you have two more equations, each containing two or more variables, you have <span style="color:#27ae60;">Systems of Equations</span>.</p>
<ul>
<li><strong>Example 1 (a set of two equations, each with two variables)</strong></li>
</ul>
<p>$$3x-5y=28$$</p>
<p>$$7x+10y=-5$$</p>
<ul>
<li><strong>Example 2 (a set of three equations, each with three variables)</strong></li>
</ul>
<p>$$3x-5y+4z=28$$</p>
<p>$$7x+10y-z=-5$$</p>
<p>$$-4x+y+z=19$$</p>
<p style="margin-left: 40px;"><strong>NOTE: </strong>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. </p>