Question

1. \

$$\begin{cases} x - y = 1 \\\\ y = 5 \\end{cases}$$

Explanation:

Step1: Substitute \( y = 5 \) into the first equation

We have the system \(

$$\begin{cases}x - y = 1\\y = 5\end{cases}$$

\). Substitute \( y = 5 \) into \( x - y = 1 \), we get \( x - 5 = 1 \).

Step2: Solve for \( x \)

To solve for \( x \), add 5 to both sides of the equation \( x - 5 = 1 \). So \( x = 1 + 5 = 6 \).

Step3: Identify the point on the graph

The solution to the system of linear equations is the point where the two lines intersect. Since \( x = 6 \) and \( y = 5 \), the point of intersection on the coordinate plane (the grid) is \((6, 5)\). To plot this, we move 6 units to the right along the \( x \)-axis (since \( x = 6 \)) and 5 units up along the \( y \)-axis (since \( y = 5 \)) from the origin \((0,0)\).

Answer:

The solution to the system of equations is \( x = 6 \), \( y = 5 \), and the point of intersection on the graph is \((6, 5)\).