Question 116993

{{{2*x-4*y=8}}} Start with the given equation



Let's test the first solution (-4,-2):



{{{2*(-4)-4*(-2)=8}}} Plug in {{{x=-4}}} and  {{{y=-2}}}



{{{0=8}}} Simplify. Since the two sides of the equation are <font size=4><b>not</b></font> equal, this means (-4,-2) is <font size=4><b>not</b></font> a solution to {{{2*x-4*y=8}}}




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




Let's test the second solution (0,-2):



{{{2*(0)-4*(-2)=8}}} Plug in {{{x=0}}} and  {{{y=-2}}}



{{{8=8}}} Simplify. Since the two sides of the equation are equal, this means (0,-2) is a solution to {{{2*x-4*y=8}}}




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




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



{{{2*(-4)-4*(0)=8}}} Plug in {{{x=-4}}} and  {{{y=0}}}



{{{-8=8}}} 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 {{{2*x-4*y=8}}}




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




Let's test the fourth solution (0,2):



{{{2*(0)-4*(2)=8}}} Plug in {{{x=0}}} and  {{{y=2}}}



{{{-8=8}}} Simplify. Since the two sides of the equation are <font size=4><b>not</b></font> equal, this means (0,2) is <font size=4><b>not</b></font> a solution to {{{2*x-4*y=8}}}



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Answer:

So the following ordered pairs are solutions to {{{2*x-4*y=8}}}


(0,-2)


Now let's graph the equation {{{2*x-4*y=8}}} and plot the points (-4,-2), (0,-2), (-4,0), and (0,2)

{{{drawing(900,900,-10,10,-10,10,
graph(900,900,-10,10,-10,10,1/2*x-2),

circle(-4,-2,0.08),
circle(-4,-2,0.10),
circle(0,-2,0.08),
circle(0,-2,0.10),
circle(-4,0,0.08),
circle(-4,0,0.10),
circle(0,2,0.08),
circle(0,2,0.10),
green(circle(0,-2,0.05)),
green(circle(0,-2,0.08)))}}}

Here we can see that the point (0,-2) lie on the line (they are the green points). These are the solutions to the equation {{{2*x-4*y=8}}}. 

Notice the other possible solutions are points that do not lie on the line. Those ordered pairs do not satisfy the equation {{{2*x-4*y=8}}}



So this means B) is the answer.