Question

1. 9x - 15y = 24

6x - 10y = -16

Explanation:

Step1: Simplify the first equation

Divide the first equation \(9x - 15y = 24\) by 3. We get \(3x - 5y = 8\). Let's call this Equation (1).

Step2: Simplify the second equation

Divide the second equation \(6x - 10y = -16\) by 2. We get \(3x - 5y = -8\). Let's call this Equation (2).

Step3: Analyze the two simplified equations

Equation (1) is \(3x - 5y = 8\) and Equation (2) is \(3x - 5y = -8\). The left - hand sides of both equations are the same (\(3x - 5y\)), but the right - hand sides are 8 and - 8, which are different. This means that the system of equations is inconsistent. In a system of linear equations \(a_1x + b_1y = c_1\) and \(a_2x + b_2y = c_2\), if \(\frac{a_1}{a_2}=\frac{b_1}{b_2}
eq\frac{c_1}{c_2}\) (where \(a_2
eq0\) and \(b_2
eq0\)), the system has no solution. Here, \(\frac{3}{3}=\frac{- 5}{-5}=1\) and \(\frac{8}{-8}=- 1\), so \(1
eq - 1\).

Answer:

The system of equations \(9x - 15y = 24\) and \(6x - 10y=-16\) has no solution.