Question 1208473
<br>
{{{4x+y=7/2}}}
{{{x^2-4xy=3}}} --> {{{x(x-4y)=3}}}<br>
The first equation contains variable y by itself, so the best algebraic approach to solving the problem is solving the first equation for y and substituting in the second equation.<br>
{{{y=-4x+7/2}}}<br>
{{{x(x-4(-4x+7/2))=3}}}
{{{x(x+16x-14)=3}}}
{{{x(17x-14)=3}}}
{{{17x^2-14x=3}}}
{{{17x^2-14x-3=0}}}
{{{(17x+3)(x-1)=0}}}<br>
x=-3/17 or x=1<br>
x=1 --> y=-4(1)+7/2=-1/2
First solution: (x,y) = (1,-1/2)<br>
x=-3/17 --> y=-4(-3/17)+7/2=12/17+7/2=24/34+119/34=143/34
Second solution: (x,y) = (-3/17,143/34)<br>
You can confirm the solutions using an online graphing utility like geogebra (geogebra.org).<br>