Can someone please help me answer these two questions? I have already answered one, and need it checked.
Give any three ordered pairs that are solutions of the equation:
1. x-y=6
(12,6)
(10,4)
(15,9)
2.-3x - 2y = 0
???
3.2x- 3y = 12
I have only one ordered pair for this:
(9,2)
2 more needed
Thanks!
-MC
It would be easier if you solve the equations for y, then plug in a value for x.
-3x - 2y = 0
add 3x to both sides
-2y = 3x
divide both sides by -2
y = (-3/2) x
Now just pick numbers for x (because of the 2 in the denominator, it will help to pick even integers).
x = 2
y = (-3/2) 2
y = -3
so (2, -3)
x = 0
y = (-3/2) 0
y = 0
so (0, 0)
x = -2
y = (-3/2)(-2)
y = 3
so (-2, 3)
Thank you Rick!!
I need two more for the third one though...
-MC
Sure, I'd be happy to help you with your questions!
To find ordered pairs that are solutions of the equation, you can plug in different values for x and y into the equation and check if they satisfy it. Let's solve each equation one by one.
1. For the equation x-y=6:
You have already found three ordered pairs, which are:
(12,6)
(10,4)
(15,9)
To check if they are solutions, substitute the x and y values into the equation:
For (12,6): 12 - 6 = 6 (satisfied)
For (10,4): 10 - 4 = 6 (satisfied)
For (15,9): 15 - 9 = 6 (satisfied)
Therefore, the three ordered pairs you found are indeed solutions to the equation x-y=6.
2. For the equation -3x - 2y = 0:
To find ordered pairs that satisfy this equation, you can pick any value for x or y and solve for the other variable. Let's choose x = 0 and solve for y:
-3(0) - 2y = 0
0 - 2y = 0
-2y = 0
y = 0
So one ordered pair that satisfies this equation is (0,0). However, this equation is linear, so it will have infinitely many solutions. This means you can choose any real values for x and plug them into the equation to get the corresponding y value.
3. For the equation 2x- 3y = 12:
You have already found one ordered pair, which is:
(9,2)
To find two more ordered pairs, you can follow a similar method as in question 2. Choose a value for x, then solve for y.
Let's choose x = 0 and solve for y:
2(0) - 3y = 12
0 - 3y = 12
-3y = 12
y = -4
The ordered pair for x = 0 is (0, -4).
Now let's choose x = 5 and solve for y:
2(5) - 3y = 12
10 - 3y = 12
-3y = 2
y = -2/3
The ordered pair for x = 5 is (5, -2/3).
Therefore, two additional ordered pairs for the equation 2x- 3y = 12 are (0, -4) and (5, -2/3).
I hope this helps! Let me know if you have any more questions.