Question 122610
{{{3*x-2*y=6}}} Start with the given equation



Let's test the first possible solution (0,-3):



{{{3*(0)-2*(-3)=6}}} Plug in {{{x=0}}} and  {{{y=-3}}}



{{{6=6}}} Simplify. Since the two sides of the equation are equal, this means (0,-3) is a solution to {{{3*x-2*y=6}}}




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




Let's test the second possible solution (0,3):



{{{3*(0)-2*(3)=6}}} Plug in {{{x=0}}} and  {{{y=3}}}



{{{-6=6}}} Simplify. Since the two sides of the equation are <font size=4><b>not</b></font> equal, this means (0,3) is <font size=4><b>not</b></font> a solution to {{{3*x-2*y=6}}}




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




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



{{{3*(-2)-2*(0)=6}}} Plug in {{{x=-2}}} and  {{{y=0}}}



{{{-6=6}}} Simplify. Since the two sides of the equation are <font size=4><b>not</b></font> equal, this means (-2,0) is <font size=4><b>not</b></font> a solution to {{{3*x-2*y=6}}}




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




Let's test the fourth  possible solution (-2,-3):



{{{3*(-2)-2*(-3)=6}}} Plug in {{{x=-2}}} and  {{{y=-3}}}



{{{0=6}}} Simplify. Since the two sides of the equation are <font size=4><b>not</b></font> equal, this means (-2,-3) is <font size=4><b>not</b></font> a solution to {{{3*x-2*y=6}}}



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Answer:

So the following ordered pairs are solutions to {{{3*x-2*y=6}}}


(0,-3)


Now let's graph the equation {{{3*x-2*y=6}}} and plot the points (0,-3), (0,3), (-2,0), and (-2,-3)

{{{drawing(900,900,-10,10,-10,10,
graph(900,900,-10,10,-10,10,3/2*x-3),

circle(0,-3,0.08),
circle(0,-3,0.10),
circle(0,3,0.08),
circle(0,3,0.10),
circle(-2,0,0.08),
circle(-2,0,0.10),
circle(-2,-3,0.08),
circle(-2,-3,0.10),
green(circle(0,-3,0.05)),
green(circle(0,-3,0.08)))}}}

Here we can see that the point (0,-3) lie on the line (it is the green point). These are the solutions to the equation {{{3*x-2*y=6}}}. 

Notice the other possible solutions are points that do not lie on the line. Those ordered pairs do not satisfy the equation {{{3*x-2*y=6}}}




So the answer is A)