which statements about the system are true? select two options.\n$y = \\frac{1}{3}x - 4$\n$3y - x = -7$\nthe…

which statements about the system are true? select two options.\n$y = \\frac{1}{3}x - 4$\n$3y - x = -7$\nthe system has one solution.\nthe system consists of parallel lines.\nboth lines have the same slope.\nboth lines have the same y - intercept.\nthe equations represent the same line.

which statements about the system are true? select two options.\n$y = \\frac{1}{3}x - 4$\n$3y - x = -7$\nthe system has one solution.\nthe system consists of parallel lines.\nboth lines have the same slope.\nboth lines have the same y - intercept.\nthe equations represent the same line.

Answer

Explanation:

Step1: Convert the second equation to slope - intercept form

Given (3y - x=-7), add (x) to both sides: (3y=x - 7). Then divide by (3): (y=\frac{1}{3}x-\frac{7}{3})

Step2: Analyze the slopes and y - intercepts

For (y = \frac{1}{3}x-4), slope (m_1=\frac{1}{3}), (y) - intercept (b_1=-4) For (y=\frac{1}{3}x-\frac{7}{3}), slope (m_2=\frac{1}{3}), (y) - intercept (b_2 =-\frac{7}{3}) Since (m_1 = m_2=\frac{1}{3}) but (b_1\neq b_2), the lines are parallel. Parallel lines have no solution (they never intersect)

Answer:

The system consists of parallel lines. Both lines have the same slope.