Question 636851
Those are linear equations.
The graph of a linear equation is a straight line.
To draw each line you just need two points.
To find a point, you just pick a value for the {{{x}}} or the {{{y}}} , and solve for the other variable.
Choose values that make the calculations and the graphing easy.
Zero is often a good choice.
Finding points to graph {{{x+y=-3}}}
When {{{x=0}}} , {{{0+y=-3}}} --> {{{highlight(y=-3)}}} .
That gives you point (0,-3).
When {{{y=0}}} , {{{x+0=-3}}} --> {{{highlight(x=-3)}}} .
That gives you point (-3,0).
Finding points to graph {{{x+y=7}}}
When {{{x=0}}} , {{{0+y=7}}} --> {{{highlight(y=7)}}} .
That gives you point (0,7).
When {{{y=0}}} , {{{x+0=7}}} --> {{{highlight(x=7)}}} .
That gives you point (7,0).
The graph (with the points circled, looks like this:
{{{drawing(300,300,-10,10,-10,10,
grid(1),
blue(circle(-3,0,0.4)),blue(circle(0,-3,0.4)),
circle(7,0,0.4),circle(0,7,0.4),
blue(line(-10,7,10,-13)), line(-10,17,10,-3)
)}}} The line for {{{x+y=-3}}} is drawn in blue.
The lines are parallel.
As a system of linear equations,
{{{system (x+y=-3,x+y=7)}}} has no solution.
That should be obvious from the start, because if {{{x+y}}} is {{{-3}}} ,
it cannot be {{{7}}} at the same time (for the same {{{x}}} and {{{y}}} ).