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Linear and Quadratic Equations · Question 17 of 66

Question 17

EasyOriginal question

What can you say about the lines 4x+6y=94x + 6y = 9 and 2x+3y=52x + 3y = 5?

Options for question 17

Show the answer and explanation
CorrectNot quiteAnswer D

Correct answer: D

Explanation

  1. Ratios: 42=2\frac{4}{2} = 2, 63=2\frac{6}{3} = 2, but 95≠2\frac{9}{5} \neq 2.

  2. Equal coefficient ratios with a different constant ratio means parallel, distinct lines.

  3. So the pair has no solution.

Worth noting

Doubling the second equation gives 4x+6y=104x + 6y = 10, which contradicts 4x+6y=94x + 6y = 9. Same slope, different lines.

Concept
Condition for parallel lines (inconsistent pair)
Typical time
40 s
Your time
—
The rule this testsPairs of linear equations
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Ten questions from Linear and Quadratic Equations, at your own pace.

Practise this chapter →

Ten questions from Linear and Quadratic Equations, at your own pace.