Question

1. solve the system \\( \

$$\begin{cases} x + y = 4 \\\\ 2x + y = 6 \\end{cases}$$

\\) using elimination. show all your work.

Explanation:

Step1: Label the equations

Let the first equation \( x + y = 4 \) be Equation (1) and the second equation \( 2x + y = 6 \) be Equation (2).

Step2: Subtract Equation (1) from Equation (2)

To eliminate \( y \), we subtract the left - hand sides and the right - hand sides of the two equations respectively.
\((2x + y)-(x + y)=6 - 4\)
Expand the left - hand side: \(2x + y-x - y=6 - 4\)
Simplify the left - hand side: \(2x - x+y - y=6 - 4\), which gives \(x = 2\)

Step3: Substitute \( x = 2 \) into Equation (1)

Substitute \(x = 2\) into \(x + y=4\), we get \(2 + y=4\)
Subtract 2 from both sides of the equation: \(y=4 - 2=2\)

Answer:

The solution of the system of equations is \(x = 2,y = 2\)