Final answer:
Points are tested for the two linear equations by substituting their coordinates into the equations. (2, 5) is not a solution to either equation, (7, 4) and (3, 6) are solutions to Equation 1, (1, 2) is a solution to Equation 2, and (6, 7) is not a solution to either equation.
Step-by-step explanation:
The subject deals with determining if a given point is a solution for one or both of the two provided linear equations. A point is a solution to a linear equation if, when substituted into the equation, it satisfies the equation (both sides of the equation are equal).
To test the point (2, 5) for Equation 1 (6x + 4y = 34), we substitute x = 2 and y = 5:
- 6(2) + 4(5) = 12 + 20 = 32, which is not equal to 34.
So point (2, 5) is not a solution to Equation 1. Now testing the same point for Equation 2 (5x – 2y = 15):
- 5(2) - 2(5) = 10 - 10 = 0, which is not equal to 15.
Therefore, point (2, 5) is not a solution to Equation 2 either. Similar steps are followed for each point with the respective equations.
- For the point (7, 4), the calculations reveal that it is a solution to Equation 1 only.
- The point (6, 7) does not satisfy either equation.
- The point (3, 6) is a solution to Equation 1 only.
- The point (1, 2) satisfies Equation 2 only.