Set 16: Systems of Equations
Explanation
What is the relationship between the lines?
The lines intersect at one point
The lines are parallel but not identical
The lines are perpendicular
The lines are identical
Detailed Explanation
Choice D is correct. Choice D is the correct answer. Step 1: Divide the first equation by 5: $$\frac{10 x - 15 y}{5} = \frac{20}{5}2x - 3 y = 4$$$ This is exactly the second equation! Conclusion: The lines are identical (coincident) This means infinitely many solutions—every point on one line is also on the other. Strategic Tip: Identical lines are also called "coincident lines" or "the same line." Choice A is incorrect because intersecting at one point requires different slopes. Choice B is incorrect because parallel but not identical would give no solution (different constants). Choice C is incorrect because both lines have slope \frac{2}{3}$, not perpendicular slopes.
Key Steps:
The correct answer is The lines are identical
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