Question

1. solve the system \\(\

$$\begin{cases} x + y = 4 \\\\ 2x + y = 5 \\end{cases}$$

\\) using elimination. show all your work.

Explanation:

Step1: Subtract the two equations

We have the system:

$$\begin{cases} x + y = 4 \quad (1)\\ 2x + y = 5 \quad (2) \end{cases}$$

Subtract equation (1) from equation (2) to eliminate \(y\):
\((2x + y) - (x + y) = 5 - 4\)
Simplify the left side: \(2x + y - x - y = x\)
Simplify the right side: \(1\)
So we get \(x = 1\).

Step2: Substitute \(x\) into equation (1)

Substitute \(x = 1\) into \(x + y = 4\):
\(1 + y = 4\)
Subtract 1 from both sides: \(y = 4 - 1 = 3\)

Answer:

The solution to the system is \(x = 1\) and \(y = 3\), or in ordered pair form \((1, 3)\).