Set 3: Systems of Equations

Choice B is correct. Choice B is the correct answer. Both equations are in slope-intercept form $y = mx + b$. Analysis: - First line: slope $m_1 = -3$, y-intercept $b_1 = 4$ - Second line: slope $m_2 = -3$, y-intercept $b_2 = -2$ Comparison: - $m_1 = m_2 = -3$ → same slope - $b_1 \neq b_2$ → different y-intercepts When lines have the same slope but different y-intercepts, they are parallel. Strategic Tip: - Parallel lines: same slope, different intercepts - Perpendicular lines: slopes are negative reciprocals ($m_1 \cdot m_2 = -1$) - Identical lines: same slope AND same intercept Choice A is incorrect because perpendicular lines have slopes that multiply to $-1$. Here, $(-3) \times (-3) = 9 \neq -1$. Choice C is incorrect because identical lines must have the same y-intercept. Choice D is incorrect because parallel lines never intersect.