Final answer:
The system of linear equations has no solution because the lines represented by the equations are parallel and will never intersect.
Step-by-step explanation:
To solve the system of linear equations:
- Arrange the equations in standard form.
9x - 15y = 24 - 6x - 10y = -16
- Multiply the second equation by -3 to eliminate x.
-3(6x - 10y) = -3(-16) - -18x + 30y = 48
- Add the two equations together.
(9x - 15y) + (-18x + 30y) = 24 + 48 - -9x + 15y = 72
- Combine like terms.
15y - 9x = 72 - Add this new equation to the first equation.
(15y - 9x) + (9x - 15y) = 72 + 24 - 0 = 96
Since the equation 0 = 96 is untrue, there is no solution to the system of linear equations. The two lines represented by the equations are parallel and will never intersect. Therefore, there is no common solution for x and y.