Class 10 Maths: Graphical Method of Solution of a Pair of Linear Equations — Practice Questions with Answers

Explanation: An inconsistent system of linear equations has no solution. Graphically, this is represented by two parallel lines that never intersect.

Explanation: The first equation simplifies to x = -1/2, which is a vertical line. The second equation simplifies to y = 5/3, which is a horizontal line. A vertical and a horizontal line intersect at exactly one point, hence there is a unique solution.

Explanation: After rewriting the equations in the standard form ax + by + c = 0, we get 2x - 5y - 6 = 0 and 6x - 15y - 18 = 0. The ratios of the coefficients are a₁/a₂ = 2/6 = 1/3, b₁/b₂ = -5/-15 = 1/3, and c₁/c₂ = -6/-18 = 1/3. Since a₁/a₂ = b₁/b₂ = c₁/c₂, the lines are coincident.

Explanation: For the given equations, the ratios of coefficients are a₁/a₂ = 1/(-3), b₁/b₂ = 2/(-6) = -1/3, and c₁/c₂ = 5/1. Since a₁/a₂ = b₁/b₂ ≠ c₁/c₂, the lines are parallel and thus have no solution.

Explanation: For the given equations, the ratio of the coefficients of x is a₁/a₂ = 3/4, and the ratio of the coefficients of y is b₁/b₂ = 2/8 = 1/4. Since a₁/a₂ ≠ b₁/b₂, the lines are intersecting.

Explanation: The equations represent two distinct horizontal lines (y=2 and y=-3) which are parallel to each other. Parallel lines never intersect, hence there is no solution.

Explanation: For a pair of linear equations to have no solution, the condition is a₁/a₂ = b₁/b₂ ≠ c₁/c₂. Here, a₁=1, b₁=1, a₂=2, b₂=k. Setting 1/2 = 1/k gives k=2.

Explanation: The equation x = a represents a vertical line parallel to the y-axis, and y = b represents a horizontal line parallel to the x-axis. These two lines intersect at the point (a, b).