Question 159294
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{{{y=2x+6}}} ----------------> eqn 1
{{{2y+3x=5}}} ---------------> eqn 2
Substitute eqn 1 in eqn 2:
{{{2(2x+6)+3x=5}}}, distribution
{{{4x+12+3x=5}}}
{{{7x=5-12=-7}}}
{{{cross(7)x/cross(7)=cross(-7)1/cross(7)}}}
{{{x=-1}}},
For {{{y}}} via eqn 1:
{{{y=2(-1)+6=-2+6}}}
{{{y=4}}}
Check it out via eqn 2:
{{{2(4)+3(-1)=5}}}
{{{8-3=5}}}
{{{5=5}}}
See graph below:
{{{drawing(300,300,-5,5,-5,5,grid(1),graph(300,300,-5,5,-5,5,(5-3x)/2,2x+6),circle(-1,4,0.1))}}} -----> see the intersection at point (-1,4). Then our answers are right.

Thank you,
Jojo