Question

1. 2x - y = -4

2x - y = 2

Explanation:

Step1: Analyze the equations

We have two linear equations: \(2x - y = -4\) and \(2x - y = 2\). Let's rewrite them in slope - intercept form (\(y=mx + b\), where \(m\) is the slope and \(b\) is the y - intercept).

For the first equation \(2x - y=-4\), we can solve for \(y\):
\(-y=-2x - 4\), multiply both sides by - 1, we get \(y = 2x+4\). The slope \(m_1 = 2\) and the y - intercept \(b_1 = 4\).

For the second equation \(2x - y = 2\), solve for \(y\):
\(-y=-2x + 2\), multiply both sides by - 1, we get \(y=2x - 2\). The slope \(m_2 = 2\) and the y - intercept \(b_2=-2\).

Step2: Determine the relationship between the lines

Since the slopes of the two lines (\(m_1 = m_2=2\)) are equal and the y - intercepts (\(b_1 = 4\) and \(b_2=-2\)) are different, the two lines are parallel. Parallel lines do not intersect, so the system of equations has no solution.

Answer:

The system of equations \(2x - y=-4\) and \(2x - y = 2\) has no solution (the two lines are parallel).