SAT Systems of two linear equations in two variables Practice Question 11 (Medium)

Question bank / Systems of two linear equations in two variables

Math · AlgebraMedium

$2x + ky = 8$
$4x + 10y = 3$
In the system of equations above, $k$ is a constant. For what value of $k$ does the system have no solution?

$2$

$5$

$10$

$20$

Show answer and explanation

Answer: B

The system has no solution when the lines are parallel and distinct. Multiplying the first equation by 2 gives $4x + 2ky = 16$ . The lines are parallel when $2k = 10$ , so $k = 5$ . Since $16 \ne 3$ , the lines are distinct.

Choice C matches the $y$ -coefficient of the second equation without accounting for the factor of 2 between the $x$ -coefficients.

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