Question

1. x - 9y = 0

x - 4y = -5

Explanation:

Step1: Subtract the two equations to eliminate \(x\)

We have the system:
\[

$$\begin{cases} x - 9y = 0 & (1)\\ x - 4y = -5 & (2) \end{cases}$$

\]
Subtract equation \((1)\) from equation \((2)\):
\[

$$\begin{align*} (x - 4y) - (x - 9y) &= -5 - 0\\ x - 4y - x + 9y &= -5\\ 5y &= -5 \end{align*}$$

\]

Step2: Solve for \(y\)

Divide both sides of \(5y = -5\) by \(5\):
\[
y=\frac{-5}{5}=-1
\]

Step3: Substitute \(y = - 1\) into equation \((1)\) to find \(x\)

Substitute \(y=-1\) into \(x - 9y = 0\):
\[

$$\begin{align*} x-9\times(-1)&=0\\ x + 9&=0\\ x&=-9 \end{align*}$$

\]

Answer:

The solution of the system is \(x = - 9\), \(y=-1\)