The system and has infinitely many solutions. What is the value of ?
Answer and explanation
Correct answer: D.
- '' adds and directly without multiplying by the scaling factor .
- '' solves and , misidentifying the proportionality scale.
- '' calculates and (), doubling the -coefficient twice.
- '' solves and , misidentifying the proportionality scale.
- '' calculates and (), doubling the -coefficient twice.
- Step 1: A linear system has infinitely many solutions when the two equations represent the exact same line, meaning their coefficients are proportional.
- Step 2: Compare the -coefficients: the second equation is scaled by . Therefore, , and .
- Step 3: Calculate the sum: .
Answer
.
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