Question 797005
{{{12= 2x + 3y}}}
If {{{x=y}}}, then I can substitute {{{x}}} for {{{y}}} and re-write the equation as
{{{12= 2x + 3x}}} --> {{{12=5x}}} --> {{{12/5=x}}} --> {{{x=2.4}}}
 
If {{{24= 4x + 8y}}} , {{{x}}} and {{{y}}} are related by that equation, and we can find some of the infinite pairs of values (x,y) that satisfy that equation.
(Finding infinite pairs would take infinite time, and I only have a few minutes until my bedtime).
24 will never be 0, or anything other than 24.
However, maybe you are thinking of finding what value of x corresponds to {{{y=0}}} for that equation, and what value of y corresponds to {{{x=0}}} for that equation.
 
{{{x=0}}}-->{{{24= 4*0+8y}}}-->{{{24=0+8y}}}-->{{{24=8y}}}-->{{{24/8=y}}}-->{{{y=3}}}
So the pair (0,3), with {{{x=0}}}and {{{y=3}}} satisfies the relation {{{24= 4x + 8y}}}
 
{{{y=0}}}-->{{{24=4x+8*0}}}-->{{{24=4x+0}}}-->{{{24=4x}}}-->{{{24/4=x}}}-->{{{x=6}}}
So the pair (6,0), with {{{x=6}}} and {{{y=0}}} satisfies the relation {{{24= 4x + 8y}}}
 
Those two data pairs, and the infinite pairs (x,y) that satisfy {{{24= 4x + 8y}}} can be graphed as
{{{drawing(300,300,-2,8,-3,7,
grid(1),
blue(circle(6,0,0.2)),blue(circle(0,3,0.2)),
blue(line(-8,7,12,-3))
)}}} Equations like {{{12= 2x + 3y}}} and {{{24= 4x + 8y}}} are called linear equations and their graphs are straight line.
 
If an equation has an x, and/or a y, and the x and/or y are at most multiplied times numbers and added or subtracted (no exponents, no x or y in a denominator, no other fancy stuff), it is a linear equation.
 
{{{blue(x=-2)}}}, {{{red(y=sqrt(3))}}}, and {{{green(y=2x+1)}}} are linear equations {{{drawing(300,300,-5,5,-5,5,
grid(0),
blue(line(-2,-5,-2,5)),
red(line(-5,sqrt(3),5,sqrt(3))),
green(line(-5,-9,5,11))
)}}}