<p><span style="font-size:22px"><a target="_blank" href="https://www.prepswift.com/quizzes/quiz/prepswift-are-2-variable-equations-solvable">Are 2-Variable Equations Solvable? Exercise</a></span></p><p>Are <span style="color:#27ae60;">$2$-Variable Equations Solvable</span>? Well, it depends. How many equations do you have? And are they different?</p>
<ul>
<li><strong>Just one equation</strong></li>
</ul>
<p style="margin-left: 40px;"><span style="color:#e74c3c;">Not solvable</span>. Take, for example, $x+y=10$. There are an infinite number of $(x,y)$ pair solutions.</p>
<ul>
<li><strong>Two distinct equations</strong></li>
</ul>
<p style="margin-left: 40px;"><span style="color:#27ae60;">Solvable</span>. For example, if your two equations are $x+y$ = 10 and $x-y=4$, you can find that $x=7$ and $y=3$. See System of Equations, Substitution Method, and Elimination Method in the following quant mountain entries.</p>
<ul>
<li><strong>Two equations but they're really the same</strong></li>
</ul>
<p style="margin-left: 40px;"><span style="color:#e74c3c;">Not solvable</span>. If we have $x+y=10$ and $2x+2y=20$, well hey that's the same equation! We just multiplied each term in the first equation by $2$ to get the second equation. So if these are the same equation, then we go back to the "not solvability" of having just one equation.</p>
<ul>
<li><strong>Two identical equations equal to different values</strong></li>
</ul>
<p style="margin-left: 40px;"><span style="color:#e74c3c;">Not solvable</span>. If you have $x+y=10$ and $x+y=13$, well that doesn't make any sense at all. (These are actually parallel lines)</p>