Question

solve the system of equations by graphing. \

$$\begin{cases} 3x - y = -4 \\\\ 2y = 6x + 2 \\end{cases}$$

options: (-1,1), infinitely many solutions, no solution, (-2,-2)

Explanation:

Step1: Rewrite equations in slope - intercept form

For the first equation \(3x - y=-4\), we can rewrite it as \(y = 3x + 4\) (by adding \(y\) to both sides and adding 4 to both sides).
For the second equation \(2y=6x + 2\), we divide both sides by 2 to get \(y = 3x+1\).

Step2: Analyze the slopes and y - intercepts

The slope - intercept form of a line is \(y=mx + b\), where \(m\) is the slope and \(b\) is the y - intercept.
For the line \(y = 3x + 4\), the slope \(m_1=3\) and the y - intercept \(b_1 = 4\).
For the line \(y=3x + 1\), the slope \(m_2 = 3\) and the y - intercept \(b_2=1\).
Since the slopes of the two lines are equal (\(m_1=m_2 = 3\)) and the y - intercepts are different (\(b_1
eq b_2\)), the two lines are parallel. Parallel lines never intersect, so the system of equations has no solution.

Answer:

No Solution