Question

Solve the system of linear equations.
9x - 15y = 24
6x - 10y = -16

Answer 1

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:

1. Arrange the equations in standard form.
   9x - 15y = 24
2. 6x - 10y = -16
3. Multiply the second equation by -3 to eliminate x.
   -3(6x - 10y) = -3(-16)
4. -18x + 30y = 48
5. Add the two equations together.
   (9x - 15y) + (-18x + 30y) = 24 + 48
6. -9x + 15y = 72
7. Combine like terms.
   15y - 9x = 72
8. Add this new equation to the first equation.
   (15y - 9x) + (9x - 15y) = 72 + 24
9. 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.