Question 633458
The coordinates of the point of intersection are the x and y that are solutions to the system
{{{system(3x + 4y =-6,2x + 5y =-11)}}}
All we have to do is solve the system.
There are many ways to do it.
Graphing the lines may suggest a solution, which we need to verify.
With just pencil and paper, that would be time consuming and cumbersome).
Probably the best way is elimination.
If we add the first equation times (-2),
{{{-6x-8y=12}}} , plus the second equation times 3,
{{{6x+15y=-33}}} , we eliminate {{{x}}} to get
{{{7y=-21}}} --> {{{highlight(y=-3)}}}
Substituting {{{y=-3}}} into {{{3x + 4y =-6}}} we get
{{{3x+4(-3)=-6}}} --> {{{3x-12=-6}}} --> {{{3x=-6+12}}} --> {{{3x=6}}} --> {{{highlight(x=2)}}}
The lines intersect at (2,-3).