Final answer:
To find out which quadrants the solutions to given systems of linear equations lie in, solve each system and locate their intersection points. After solving, the match-ups are 1 with quadrant I, 2 with quadrant II, 3 with quadrant I again, and 4 with quadrant III.
Step-by-step explanation:
We need to find out in which quadrants the solutions to the given systems of linear equations lie. To do so, we need to solve each system and determine where their intersection points are located relative to the x and y axes on a coordinate plane.
- For the system 3x - 2y = 10 and 5x + 3y = 4, let's solve them simultaneously to find the intersection point:
By using either substitution or elimination method, we can determine that the solution lies in quadrant I, where both x and y are positive.
- Similarly, for the system 3x + 2y = 14 and x - 3y = -10, solving them shows that the solution lies in quadrant II, where x is negative and y is positive.
- The system x + 2y = 8 and 4x + 6y = 22 has a solution in quadrant I as well.
- Finally, the system 2x + 3y = -12 and 4x - 2y = -2 has a solution in quadrant III, where both x and y are negative.
Therefore, the matches are:
- 1 - b. I
- 2 - d. II
- 3 - b. I
- 4 - a. III