Select the order pairs that are solutions to the equation below
2x+3y=—12
(0,-4)
(2,-1)
(0, 0)
(—6,0)
To determine which of the ordered pairs are solutions to the equation, we can substitute the values of x and y into the equation and see if it holds true.
Using the ordered pair (0,-4):
2(0) + 3(-4) = 0 + (-12) = -12
Since -12 equals -12, the equation holds true for (0,-4).
Using the ordered pair (2,-1):
2(2) + 3(-1) = 4 + (-3) = 1
Since 1 does not equal -12, the equation does not hold true for (2,-1).
Using the ordered pair (0,0):
2(0) + 3(0) = 0 + 0 = 0
Since 0 does not equal -12, the equation does not hold true for (0,0).
Using the ordered pair (—6,0):
2(-6) + 3(0) = -12 + 0 = -12
Since -12 equals -12, the equation holds true for (—6,0).
Therefore, the ordered pairs that are solutions to the equation are:
(0,-4) and (-6,0).
To check if an ordered pair is a solution to the equation 2x + 3y = -12, substitute the values of x and y into the equation and see if it satisfies the equation. Let's check each ordered pair:
(0, -4):
2(0) + 3(-4) = 0 + (-12) = -12
The equation is satisfied, so (0, -4) is a solution.
(2, -1):
2(2) + 3(-1) = 4 + (-3) = 1
The equation is not satisfied, so (2, -1) is not a solution.
(0, 0):
2(0) + 3(0) = 0 + 0 = 0
The equation is not satisfied, so (0, 0) is not a solution.
(-6, 0):
2(-6) + 3(0) = (-12) + 0 = -12
The equation is satisfied, so (-6, 0) is a solution.
Therefore, the ordered pairs that are solutions to the equation 2x + 3y = -12 are:
(0, -4)
(-6, 0)
To determine if a pair of numbers is a solution to the equation 2x + 3y = -12, we need to substitute the values of x and y into the equation and check if the equation is true. Let's check each ordered pair:
1. (0, -4):
Substituting x = 0 and y = -4 into the equation, we get:
2(0) + 3(-4) = 0 - 12 = -12
The equation is true. So, (0, -4) is a solution to the equation.
2. (2, -1):
Substituting x = 2 and y = -1 into the equation, we get:
2(2) + 3(-1) = 4 - 3 = 1
The equation is not true. So, (2, -1) is not a solution to the equation.
3. (0, 0):
Substituting x = 0 and y = 0 into the equation, we get:
2(0) + 3(0) = 0 + 0 = 0
The equation is not true. So, (0, 0) is not a solution to the equation.
4. (-6, 0):
Substituting x = -6 and y = 0 into the equation, we get:
2(-6) + 3(0) = -12 + 0 = -12
The equation is true. So, (-6, 0) is a solution to the equation.
Based on the above analysis, the ordered pairs that are solutions to the equation 2x + 3y = -12 are:
(0, -4) and (-6, 0).