(i) No solution: A system of linear equations has no solution if the lines are parallel, which means they have the same slope. The slope of a line in the form ax + by = c is -a/b. So, for the given system, the slopes are -9/k and -k. For no solution, these should be equal. So, -9/k = -k. Solving this gives k^2 = 9, so k = ±3.

(ii) Infinite number of solutions: A system of linear equations has an infinite number of solutions if the lines coincide, which means they are the same line. This happens when the ratios of the coefficients of x, y and the constant term are equal in both equations. So, 9/k = k/1 = 9/-3. Solving this gives k^2 = 9 and k = -3.

(iii) A unique solution: A system of linear equations has a unique solution if the lines intersect at a single point. This happens when the slopes are not equal. From (i), we know that the slopes are equal when k = ±3. So, for a unique solution, k ≠ ±3.

Question

(i) No solution: A system of linear equations has no solution if the lines are parallel, which means they have the same slope. The slope of a line in the form ax + by = c is -a/b. So, for the given system, the slopes are -9/k and -k. For no solution, these should be equal. So, -9/k = -k. Solving this gives k^2 = 9, so k = ±3.

(ii) Infinite number of solutions: A system of linear equations has an infinite number of solutions if the lines coincide, which means they are the same line. This happens when the ratios of the coefficients of x, y and the constant term are equal in both equations. So, 9/k = k/1 = 9/-3. Solving this gives k^2 = 9 and k = -3.

(iii) A unique solution: A system of linear equations has a unique solution if the lines intersect at a single point. This happens when the slopes are not equal. From (i), we know that the slopes are equal when k = ±3. So, for a unique solution, k ≠ ±3.

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(i) No solution: A system of linear equations has no solution if the lines are parallel, which means they have the same slope. The slope of a line in the form ax + by = c is -a/b. So, for the given system, the slopes are -9/k and -k. For no solution, these should be equal. So, -9/k = -k. Solving this gives k^2 = 9, so k = ±3.

(ii) Infinite number of solutions: A system of linear equations has an infinite number of solutions if the lines coincide, which means they are the same line. This happens when the ratios of the coefficients of x, y and the constant term are equal in both equations. So, 9/k = k/1 = 9/-3. Solving this gives k^2 = 9 and k = -3.

(iii) A unique solution: A system of linear equations has a unique solution if the lines intersect at a single point. This happens when the slopes are not equal. From (i), we know that the slopes are equal when k = ±3. So, for a unique solution, k ≠ ±3.

Determine k so that the system 9x + ky = 9; kx + y = −3 has (i) no solution; (ii) infinite number of solutions; (iii) a unique solution.

Question

Determine k so that the system

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