Question 105280

{{{x+3*y=10}}} Start with the given equation



Let's test the first solution (7,1):



{{{(7)+3*(1)=10}}} Plug in {{{x=7}}} and  {{{y=1}}}



{{{10=10}}} Simplify. Since the two sides of the equation are equal, this means (7,1) is a solution to {{{x+3*y=10}}}




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




Let's test the second solution (10,0):



{{{(10)+3*(0)=10}}} Plug in {{{x=10}}} and  {{{y=0}}}



{{{10=10}}} Simplify. Since the two sides of the equation are equal, this means (10,0) is a solution to {{{x+3*y=10}}}




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




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



{{{(1)+3*(-3)=10}}} Plug in {{{x=1}}} and  {{{y=-3}}}



{{{-8=10}}} Simplify. Since the two sides of the equation are <font size=4><b>not</b></font> equal, this means (1,-3) is <font size=4><b>not</b></font> a solution to {{{x+3*y=10}}}




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




Let's test the fourth solution (-8,6):



{{{(-8)+3*(6)=10}}} Plug in {{{x=-8}}} and  {{{y=6}}}



{{{10=10}}} Simplify. Since the two sides of the equation are equal, this means (-8,6) is a solution to {{{x+3*y=10}}}



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Answer:

So the following ordered pairs are solutions to {{{x+3*y=10}}}


(7,1), (10,0), and (-8,6)


Now let's graph the equation {{{x+3*y=10}}} and plot the points (7,1), (10,0), (1,-3), and (-8,6)

{{{drawing(900,900,-10,13,-10,10,
graph(900,900,-10,13,-10,10,-1/3*x+10/3),

circle(7,1,0.08),
circle(7,1,0.10),
circle(10,0,0.08),
circle(10,0,0.10),
circle(1,-3,0.08),
circle(1,-3,0.10),
circle(-8,6,0.08),
circle(-8,6,0.10),
green(circle(7,1,0.05)),
green(circle(7,1,0.08)),
green(circle(10,0,0.05)),
green(circle(10,0,0.08)),
green(circle(-8,6,0.05)),
green(circle(-8,6,0.08)))}}}

Here we can see that the points (7,1), (10,0), and (-8,6) lie on the line (they are the green points). These are the solutions to the equation {{{x+3*y=10}}}. 

Notice the other possible solutions are points that do not lie on the line. Those ordered pairs do not satisfy the equation {{{x+3*y=10}}}