Find the missing coordinate to complete the ordered-pair solution to the given linear equation.
2x−3y=3
(a) (−3, )
(b) ( ,1)
in the first, replace x with -3 and solve for y
in the second, replace y with 1 and solve for x
Y=1/3x-7; (-9,), (,-5)
To find the missing coordinate, we need to substitute the given coordinate into the equation and solve for the missing variable.
Let's consider the first option: (−3, ). Here, the x-coordinate is -3 and the y-coordinate is missing. So, we substitute x = -3 into the equation:
2x - 3y = 3
2(-3) - 3y = 3
-6 - 3y = 3
Next, we solve for y:
-3y = 3 + 6
-3y = 9
y = -3
Therefore, the missing coordinate to complete the ordered-pair solution to the equation 2x - 3y = 3 is (-3, -3).
Now, let's consider the second option: ( ,1). Here, the x-coordinate is missing and the y-coordinate is 1. So, we substitute y = 1 into the equation:
2x - 3y = 3
2x - 3(1) = 3
2x - 3 = 3
Next, we solve for x:
2x = 3 + 3
2x = 6
x = 3
Therefore, the missing coordinate to complete the ordered-pair solution to the equation 2x - 3y = 3 is (3, 1).
In conclusion, the missing coordinate for option (a) is (-3, -3) and the missing coordinate for option (b) is (3, 1).
To find the missing coordinate, we need to substitute the given ordered-pair solution into the linear equation and solve for the missing variable.
Let's start with option (a) (-3, y).
We have -3 as the x-coordinate and y as the missing y-coordinate.
Substituting these values into the equation 2x - 3y = 3, we get:
2(-3) - 3y = 3
-6 - 3y = 3
Now, we can solve for y:
Subtracting -6 from both sides:
-3y = 9
Dividing both sides by -3:
y = -3
Therefore, the missing coordinate for option (a) is (-3, -3).
Now let's move on to option (b) (x, 1).
We have x as the missing x-coordinate and 1 as the y-coordinate.
Substituting these values into the equation 2x - 3y = 3, we get:
2x - 3(1) = 3
2x - 3 = 3
Now, we can solve for x:
Adding 3 to both sides:
2x = 6
Dividing both sides by 2:
x = 3
Therefore, the missing coordinate for option (b) is (3, 1).
To summarize, the missing coordinates to complete the ordered-pair solutions are:
(a) (-3, -3)
(b) (3, 1)