Question

1. solve the system of equations \\(\

$$\begin{cases} 2x + 3y = -5 \\\\ 7x - 3y = 23 \\end{cases}$$

\\) by the best method. explain your choice.

Explanation:

Step1: Choose Elimination Method

The system has \(+3y\) and \(-3y\), so elimination (adding equations) eliminates \(y\).
Add the two equations: \((2x + 3y)+(7x - 3y)=-5 + 23\)
Simplify: \(9x=18\)

Step2: Solve for \(x\)

Divide both sides by 9: \(x=\frac{18}{9}=2\)

Step3: Substitute \(x = 2\) into first equation

Substitute into \(2x + 3y=-5\): \(2(2)+3y=-5\)
Simplify: \(4 + 3y=-5\)
Subtract 4: \(3y=-5 - 4=-9\)
Divide by 3: \(y=\frac{-9}{3}=-3\)

Answer:

The solution to the system is \(x = 2\), \(y=-3\) (or the ordered pair \((2, -3)\))