# find four solutions of the equation write the solutions as order pairs y=-3x-6

y=-3x-6

To find four solutions , we will substitute x with any real number and calculate y value:

1) when x= 1 ==> y=-3(1)-6 = -3-6=-9

Or the pair (1,-9) is a solution

2) When x= 2 ==> y= -3(2)-6= -12

or the pair (2,-12) is a solution.

3) When x= -3  ==> y=-3(-3)-6 = 3

or the pair (-3, 3) is a solution

4) When x= -2 ==> y= -3(-2)-6= 0\

or the pair (-2,0) is a solution.

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We can answer this question by constructing a table of values, picking values for x, substituting those values in, and calculating the y value - frequently people like to use a table that looks like this

x|-3x-6   |y ordered pair is (x,y)

0|-3*0-6 |-6 ordered pair is (0,-6)

1|-3*1-6 |-9 ordered pair is (1,-9)

2|-3*2-6 |-12 ordered pair is (2,-12)

3|-3*3-6|-15 ordered pair is (3,-15)

4 solutions to the equation written as ordered pairs are (0,-6), (1,-9), (2,-12), (3,-15) These solutions can be checked by substituting both the x and y value into the original equation and doing the calculations. Both sides of the equation should end up the same, like this.

-15=-3*3-6 =>-9-6=>-15 and -15=-15 checks

please note, there are an infinite number of possible solutions. I chose 4 easy to work with small integers, but any integers could have been chosen to use for x. You could pick, 5, 6, 8, 15, 23, 105, -2, -10, etc...any numbers, and you would have gotten the corresponding y value, for instance, x = -10 then -3*-10-6 => 30-6 => 24 so the ordered pair solution for x = -10 would be (-10,24)

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