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

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### 4 Answers

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)

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.

A solution for the equation above is a point which belongs to the graph of the equation.

Let's calculate first the intercepts of the graph with the x and y axis.

For interception with x axis, we'll put y=0.

0=-3x-6

We'll add 3x both sides:

3x = 6

We'll divide by 3:

x = 2

The interception point is: (2,0).

The interception point with y axis is:

y=-3x-6

y=-3*0-6

y = -6

The interception point is: (0,-6).

To find another point, we just have to give real values to x and we'll find out the corresponding values for y.

Let's put x=1 and we'll calculate y:

y = -3x-6

y = -3*1-6

y = -3-6

y = -9

Another point on the graph is: (1,-9).

Let's give another value to x, namely x=-1:

y = -3*(-1)-6

y = 3-6

y = -3

The fourth point on the graph is: (-1,-3).

To find 4 solutions of the equation y = -3x-6.

Solution:

To get a solution of the equation, y = = -3x - 6, we put an arbitrary value for x , say x=a , and then obtain the corresponding value of y as y = -3a-6 from the equation.

For x = 0, we get from the equation y = -3*0-6 = -6. So the ordered pair solution is (0,-6)

F0x =5, y = -3*5 - 6 = -9. Therefore, (5,-9) is a solution.

When x = 10, y = -30 -3 = -33. So (10, -33) is asolution).

When x= -8, y = -3*(-8) -3 = 24 - 3 = 21. Now (-8 , 21) is a solution.