Question

1. \

$$\begin{cases} 2x + y = 8 \\\\ x = 5 \\end{cases}$$

Explanation:

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

We have the system of equations \(

$$\begin{cases}2x + y = 8\\x = 5\end{cases}$$

\). Substitute \( x = 5 \) into \( 2x + y = 8 \), we get \( 2\times5 + y = 8 \), which simplifies to \( 10 + y = 8 \).

Step2: Solve for \( y \)

Subtract 10 from both sides of the equation \( 10 + y = 8 \): \( y = 8 - 10 = - 2 \). So the solution of the system is \( x = 5 \), \( y = - 2 \), and the solution point is \( (5, - 2) \). To graph this, the line \( x = 5 \) is a vertical line passing through \( x = 5 \) on the x - axis. For the line \( 2x + y = 8 \), we can rewrite it as \( y=-2x + 8 \). When \( x = 0 \), \( y = 8 \); when \( y = 0 \), \( x = 4 \). Plot these two lines, and their intersection point is \( (5, - 2) \).

Answer:

The solution of the system of equations is \( x = 5 \), \( y=-2 \) (or the ordered pair \((5, - 2)\)).