Final answer:
To find the solutions to the linear equation 7x - 12y = -3, given ordered pairs need to be tested by substitution in the equation. The pairs that satisfy the equation are b. (3,2) and d. (-9,-5).
Step-by-step explanation:
The question is asking us to select all of the ordered pairs (x,y) that satisfy the linear equation 7x - 12y = -3. To verify if an ordered pair is a solution to the equation, we substitute the x and y values into the equation and check if the equation holds true. Let's apply this method to each given pair:
- For pair a. (-4, 6), substituting x = -4 and y = 6 gives us 7(-4) - 12(6) = -28 - 72 ≠ -3. So this pair is not a solution.
- For pair b. (3,2), substituting x = 3 and y = 2 gives us 7(3) - 12(2) = 21 - 24 = -3. This pair is a solution.
- For pair c. (-2, -1), substituting x = -2 and y = -1 gives us 7(-2) - 12(-1) = -14 + 12 = -2 ≠ -3. So this pair is not a solution.
- For pair d. (-9,-5), substituting x = -9 and y = -5 gives us 7(-9) - 12(-5) = -63 + 60 = -3. This pair is a solution.
- For pair e. (-4, -2), substituting x = -4 and y = -2 gives us 7(-4) - 12(-2) = -28 + 24 = -4 ≠ -3. So this pair is not a solution.
Thus, the correct ordered pairs that are solutions to the equation are b. (3,2) and d. (-9,-5).