Question 112863


{{{x-y=4}}} Start with the given equation



Let's test the first solution (3,1):



{{{(3)-(1)=4}}} Plug in {{{x=3}}} and  {{{y=1}}}



{{{2=4}}} Simplify. Since the two sides of the equation are <font size=4><b>not</b></font> equal, this means (3,1) is <font size=4><b>not</b></font> a solution to {{{x-y=4}}}




-------Now lets test another solution-------




Let's test the second solution (0,-4):



{{{(0)-(-4)=4}}} Plug in {{{x=0}}} and  {{{y=-4}}}



{{{4=4}}} Simplify. Since the two sides of the equation are equal, this means (0,-4) is a solution to {{{x-y=4}}}




-------Now lets test another solution-------




Let's test the third solution (-4,0):



{{{(-4)-(0)=4}}} Plug in {{{x=-4}}} and  {{{y=0}}}



{{{-4=4}}} Simplify. Since the two sides of the equation are <font size=4><b>not</b></font> equal, this means (-4,0) is <font size=4><b>not</b></font> a solution to {{{x-y=4}}}




-------Now lets test another solution-------




Let's test the fourth solution (-3,-7):



{{{(-3)-(-7)=4}}} Plug in {{{x=-3}}} and  {{{y=-7}}}



{{{4=4}}} Simplify. Since the two sides of the equation are equal, this means (-3,-7) is a solution to {{{x-y=4}}}



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Answer:

So the following ordered pairs are solutions to {{{x-y=4}}}


(0,-4) and  (-3,-7) 


Now let's graph the equation {{{x-y=4}}} and plot the points (3,1), (0,-4), (-4,0), and (-3,-7)

{{{drawing(900,900,-10,10,-10,10,
graph(900,900,-10,10,-10,10,x-4),

circle(3,1,0.08),
circle(3,1,0.10),
circle(0,-4,0.08),
circle(0,-4,0.10),
circle(-4,0,0.08),
circle(-4,0,0.10),
circle(-3,-7,0.08),
circle(-3,-7,0.10),
green(circle(0,-4,0.05)),
green(circle(0,-4,0.08)),
green(circle(-3,-7,0.05)),
green(circle(-3,-7,0.08)))}}}

Here we can see that the points (0,-4) and  (-3,-7)  lie on the line (they are the green points). These are the solutions to the equation {{{x-y=4}}}. 

Notice the other possible solutions are points that do not lie on the line. Those ordered pairs do not satisfy the equation {{{x-y=4}}}