Question 793217
I would first multiply both sides of the equal sign times 10 (in both equations) to get
{{{system(3x+y=7,4x-4y=12)}}}
The second equation can be simplified by dividing both sides by 4 to get
{{{x-y=3}}}
{{{3x+y=7}}}-->{{{y=7-3x}}} and substituting into {{{x-y=3}}} we get
{{{x-(7-3x)=3}}}-->{{{x-7+3x=3}}}-->{{{x+x=3+7}}}-->{{{2x=10}}}-->{{{x=10/2}}}-->{{{highlight(x=5/2)}}}
Then substituting into {{{y=7-3x}}}, we get
{{{y=7-3*(5/2)}}}-->{{{y=7-15/2}}}-->{{{y=14/2-15/2}}}-->{{{highlight(y=-1/2)}}}
 
{{{3x+y=7}}}-->{{{y=7-3x}}} goes through the points
(0,7) because {{{x=0}}} means {{{y=7-3*0=7-0=7}}} and
(3,-2) because {{{x=3}}} means {{{y=7-3*3=7-9=-2}}}
{{{x-y=3}}} goes through the points
(0,-3) because {{{x=0}}} means {{{0-y=-3}}}-->{{{-y=-3}}}-->{{{y=3}}} and
(3,0) because {{{y=0}}} means {{{x-0=3}}}-->{{{x=3}}}
Plotting the two points found for each line and connecting then, we get
{{{drawing(300,300,-5,5,-3,7,grid(1),
blue(circle(0,7,0.3)),blue(circle(3,-2,0.3)),blue(line(0,7,4,-5)),
green(circle(0,-3,0.3)),green(circle(3,0,0.3)),green(line(5,2,-5,-8))
)}}}