Question 110657


{{{x+2*y=9}}} Start with the given equation



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



{{{(7)+2*(1)=9}}} Plug in {{{x=7}}} and  {{{y=1}}}



{{{9=9}}} Simplify. Since the two sides of the equation are equal, this means (7,1) is a solution to {{{x+2*y=9}}}




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




Let's test the second solution (9,0):



{{{(9)+2*(0)=9}}} Plug in {{{x=9}}} and  {{{y=0}}}



{{{9=9}}} Simplify. Since the two sides of the equation are equal, this means (9,0) is a solution to {{{x+2*y=9}}}




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




Let's test the third solution (5,-2):



{{{(5)+2*(-2)=9}}} Plug in {{{x=5}}} and  {{{y=-2}}}



{{{1=9}}} Simplify. Since the two sides of the equation are <font size=4><b>not</b></font> equal, this means (5,-2) is <font size=4><b>not</b></font> a solution to {{{x+2*y=9}}}




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




Let's test the fourth solution (-7,8):



{{{(-7)+2*(8)=9}}} Plug in {{{x=-7}}} and  {{{y=8}}}



{{{9=9}}} Simplify. Since the two sides of the equation are equal, this means (-7,8) is a solution to {{{x+2*y=9}}}



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Answer:

So the following ordered pairs are solutions to {{{x+2*y=9}}}


(7,1), (9,0), and (-7,8)


Now let's graph the equation {{{x+2*y=9}}} and plot the points (7,1), (9,0), (5,-2), and (-7,8)

{{{drawing(900,900,-10,10,-10,10,
graph(900,900,-10,10,-10,10,-1/2*x+9/2),

circle(7,1,0.08),
circle(7,1,0.10),
circle(9,0,0.08),
circle(9,0,0.10),
circle(5,-2,0.08),
circle(5,-2,0.10),
circle(-7,8,0.08),
circle(-7,8,0.10),
green(circle(7,1,0.05)),
green(circle(7,1,0.08)),
green(circle(9,0,0.05)),
green(circle(9,0,0.08)),
green(circle(-7,8,0.05)),
green(circle(-7,8,0.08)))}}}

Here we can see that the points (7,1), (9,0), and (-7,8) lie on the line (they are the green points). These are the solutions to the equation {{{x+2*y=9}}}. 

Notice the other possible solutions are points that do not lie on the line. Those ordered pairs do not satisfy the equation {{{x+2*y=9}}}