Question 1000327
1. Determine if (5/6, -2) is a solution to -6x-7y=9
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{{{-6x-7y=9}}} Start with the given equation.



{{{-6(5/6)-7(-2)=9}}} Replace x with 5/6. Replace y with -2



{{{-5+14=9}}} Multiply



{{{9=9}}} Add. This equation is true



The last equation is true, so {{{-6x-7y=9}}} is true when (x,y) = (5/6, -2)



Therefore, (5/6, -2) is a solution to {{{-6x-7y=9}}}



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2.Given the linear equation y = -2/3x +1. Find the y - coordinates of the points (-6, ), (-3, ) and (3, )
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Plug in x = -6



{{{y = (-2/3)x + 1}}} Start with the given equation



{{{y = (-2/3)(-6) + 1}}} Replace every {{{x}}} with {{{-6}}}



{{{y = 4 + 1}}} Multiply



{{{y = 5}}} Add



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Plug in x = -3



{{{y = (-2/3)x + 1}}} Start with the given equation



{{{y = (-2/3)(-3) + 1}}} Replace every {{{x}}} with {{{-3}}}



{{{y = 2 + 1}}} Multiply



{{{y = 3}}} Add



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Plug in x = 3



{{{y = (-2/3)x + 1}}} Start with the given equation



{{{y = (-2/3)(3) + 1}}} Replace every {{{x}}} with {{{3}}}



{{{y = -2 + 1}}} Multiply



{{{y = -1}}} Add



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So the ordered pairs are (-6,<font size=4 color="red">5</font>), (-3,<font size=4 color="red">3</font>), and (3,<font size=4 color="red">-1</font>)