Question 1092356
<br>When both equations are given to you in the form Ax+By=C, by far the easiest way to solve the system of equations is by eliminating one of the variables.<br>
You are given
{{{3x-y = -6}}}
{{{2x+3y = 7}}}<br>
Since the y terms have coefficients that are opposite signs, my preference is to multiply one or both equations by appropriate constants so that the coefficients of y in the two equations are opposites; then adding the two equations will eliminate y, leaving an equation in just x that I can solve.  Then I use that value of x in one of the original equations to solve for y.<br>
{{{9x-3y = -18}}}  [multiply the first equation by 3]
{{{2x+3y = 7}}}
{{{11x = -11}}}  [add the two equations]
{{{x = -1}}}
{{{2(-1)+3y = 7}}}  [set x to -1 in the second equation]
{{{-2+3y = 7}}}
{{{3y = 9}}}
{{{y = 3}}}<br>
The solution is (x,y) = (-1,3).