Pair of Linear Equations in Two Variables : Grade X NCERT

Explain standard form of a pair of linear equations in two variables and the graphical method, showing when lines intersect, are parallel, or coincide, yielding one, none, or infinite solutions.

Explore solving pair of linear equations in two variables using the graphical method, by plotting lines and finding their intersection as the solution. Learn about dependent and inconsistent cases.

Analyze how two linear equations in two variables create lines on the x–y plane and reveal three cases: a unique solution, no solution, or many solutions.

Compare coefficients of a pair of linear equations to decide if the system has a unique solution, infinitely many, or none, using ratio patterns.

Compare coefficients of a pair of linear equations in two variables using ratios. Graph the equations to identify intersecting lines with one solution or coincident lines with infinitely many solutions.

Use substitution to solve a pair of linear equations by expressing one variable in terms of the other and substituting into the second equation, noting unique, infinite, or no solution.

Apply the elimination method to solve two linear equations, cancel a variable by matching coefficients, verify results by substitution, and identify parallel lines or many solutions.

Apply the elimination method to a two-digit number problem: represent the digits as x and y, use the reverse and sum conditions to solve for x and y.

Learn the cross multiplication method for solving pair of linear equations in two variables, derive x and y, and recognize cases with zero denominators indicating no or infinite solutions.

Learn to solve a pair of linear equations in two variables using the cross multiplication method, applying standard form and crisscross steps with a worked example.

Explore the cross multiplication method to solve a system of two linear equations, convert word problems to equations, and determine when solutions are unique or infinitely many solutions.

Shows how to reduce equations to a pair of linear equations in two variables, using substitution and elimination, with examples converting 1/x and 1/y to B and Q.

Solve a pair of linear equations in two variables by modeling upstream and downstream boat speeds using still-water and stream speeds, and verify with 10 and 13 hour trips.