For what value of k does the system 2x + ky = 8 and kx + 8y = 16 have infinitely many solutions?

k = 4 only Need scalar match: \frac{2}{k} = \frac{k}{8} = \frac{8}{16} = \frac{1}{2}. From k/8 = 1/2: k = 4. Check 2/k = 2/4 = 1/2. ✓ So k = 4.

Systems of Two Linear Equations in Two Variables

SAT Math· difficulty 4/5

k

Explanation

\frac{2}{k} = \frac{k}{8} = \frac{8}{16} = \frac{1}{2}

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