Question

1. solve the system of equations \\(\

$$\begin{cases} 2x + y = 8 \\\\ x - y = 10 \\end{cases}$$

\\)

Explanation:

Step1: Add the two equations to eliminate \( y \)

We have the system of equations:
\[

$$\begin{cases} 2x + y = 8 \\ x - y = 10 \end{cases}$$

\]
Adding the left - hand sides and the right - hand sides of the two equations respectively: \((2x + y)+(x - y)=8 + 10\)
Simplifying the left - hand side: \(2x+y+x - y=3x\), and the right - hand side is \(18\). So we get the equation \(3x=18\).

Step2: Solve for \( x \)

From \(3x = 18\), divide both sides of the equation by \(3\): \(x=\frac{18}{3}=6\)

Step3: Substitute \( x = 6 \) into one of the original equations to solve for \( y \)

Substitute \(x = 6\) into the second equation \(x - y=10\), we get \(6 - y=10\)
Subtract \(6\) from both sides: \(-y=10 - 6=4\)
Multiply both sides by \(- 1\): \(y=-4\)

Answer:

The solution of the system of equations is \(x = 6,y=-4\)