determine which of the ordered pairs are solutions to the given equation 3x-2y=12 , (2,-3) (4,-2) (6,3) (5, 15/2)
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To determine which ordered pairs are solutions to the equation 3x-2y=12, we can substitute the x and y values of each pair into the equation and check if the equation holds true.
Let's start with the first ordered pair (2, -3):
Substituting x=2 and y=-3 into the equation:
3(2) - 2(-3) = 6 + 6 = 12
Since the equation holds true, (2, -3) is a solution to the equation.
Moving on to the second ordered pair (4, -2):
Substituting x=4 and y=-2 into the equation:
3(4) - 2(-2) = 12 + 4 = 16
The equation does not hold true, so (4, -2) is not a solution to the equation.
Next, let's consider the third ordered pair (6, 3):
Substituting x=6 and y=3 into the equation:
3(6) - 2(3) = 18 - 6 = 12
The equation holds true, so (6, 3) is a solution to the equation.
Finally, we have the fourth ordered pair (5, 15/2):
Substituting x=5 and y=15/2 into the equation:
3(5) - 2(15/2) = 15 - 15 = 0
The equation does not hold true, so (5, 15/2) is not a solution to the equation.
In summary, the ordered pairs (2, -3) and (6, 3) are solutions to the equation 3x-2y=12.
Put x coordinate into equation:
3 x - 2 y = 12
and check y coordinate
1. For x = 2
3 x - 2 y = 3 * 2 - 2 y = 12
6 - 2 y = 12 Subtact 6 to both sides
6 - 2 y - 6 = 12 - 6
- 2 y = 6 Divide both sides by - 2
y = 6 / - 2
y = - 3
x = 2 , y = - 3 True
2. For x = 4
3 x - 2 y = 3 * 4 - 2 y = 12
12 - 2 y = 12 Subtact 12 to both sides
12 - 2 y - 12 = 12 - 12
- 2 y = 0
y = 0
x = 4 , y = 0 False
3. For x = 6
3 x - 2 y = 3 * 6 - 2 y = 12
18 - 2 y = 12 Subtact 18 to both sides
18 - 2 y - 18 = 12 - 18
- 2 y = - 6 Divide both sides by - 2
y = - 6 / - 2
y = 3
x = 6 , y = 3 True
4. For x = 5
3 x - 2 y = 3 * 5 - 2 y = 12
15 - 2 y = 12 Subtact 15 to both sides
15 - 2 y - 15 = 12 - 15
- 2 y = - 3 Divide both sides by - 2
y = - 3 / - 2
y = 3 / 2
x = 5 , y = 3 / 2 False
The ordered pairs are:
( 2 , - 3 ) and ( 6 , 3 )