Pair of Linear Equations in Two Variables

Solve by elimination method: 2x + 3y = 11 and 2x - 4y = -24. [CBSE 2025]

For what value of k will equations x + 2y = 5 and 3x + ky + 1 = 0 have infinitely many solutions? [CBSE 2024]

Solve graphically: x + y = 5 and x - y = 3. [CBSE 2023]

The sum of digits of a two-digit number is 9. If 27 is added to it, digits are reversed. Find the number. [CBSE 2022]

Solve by substitution: 3x - y = 3 and 9x - 3y = 9. [CBSE 2021]

a₁x + b₁y + c₁ = 0\na₂x + b₂y + c₂ = 0

Unique solution: a₁/a₂ ≠ b₁/b₂\nInfinitely many: a₁/a₂ = b₁/b₂ = c₁/c₂\nNo solution: a₁/a₂ = b₁/b₂ ≠ c₁/c₂

x/(b₁c₂-b₂c₁) = y/(c₁a₂-c₂a₁) = 1/(a₁b₂-a₂b₁)

Step 1: Make coefficients of one variable equal by multiplying equations. Step 2: Add or subtract to eliminate that variable. Step 3: Solve for remaining variable. Step 4: Substitute back to find other variable.

For a₁x+b₁y+c₁=0 and a₂x+b₂y+c₂=0: If a₁/a₂ ≠ b₁/b₂, lines intersect (unique solution). If a₁/a₂ = b₁/b₂ = c₁/c₂, lines coincide (infinite solutions). If a₁/a₂ = b₁/b₂ ≠ c₁/c₂, lines are parallel (no solution).

1. Make coefficients of one variable equal\n2. Add or subtract equations to eliminate that variable\n3. Solve for remaining variable\n4. Substitute back to find other variable

1. Express one variable in terms of other from one equation\n2. Substitute in second equation\n3. Solve for one variable\n4. Find other variable