Homeclass 10MathsPair of Linear Equations in Two VariablesElimination Method

Elimination Method

The elimination method is an algebraic technique used to solve a pair of linear equations in two variables. It involves multiplying one or both equations by suitable constants to equalize the coefficients of one variable, then adding or subtracting the equations to eliminate that variable and solve for the other.

Key Concepts

First, ensure both linear equations are written in the standard form ax + by = c.
Multiply one or both equations by non-zero constants so that the coefficients of either x or y become numerically equal.
Add or subtract the resulting equations to eliminate one variable, solve for the remaining variable, and substitute this value back into an original equation to find the second variable.

Formula & Equation

For equations a1x + b1y = c1 and a2x + b2y = c2, multiply the first by b2 and the second by b1, then subtract to eliminate y.

x and y are the unknown variables, a1, a2, b1, b2 are their respective coefficients, and c1, c2 are the constant terms.

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Common Misconceptions

Myth: Forgetting to multiply the constant term on the right side of the equal sign when adjusting the coefficients.
Fact: The multiplication property of equality requires that every term on both the left and right sides of the equation must be multiplied by the chosen constant to keep the equation balanced.

Real World Applications

Determining the fixed charge and per-kilometer charge of a taxi service by comparing two different journey distances and their total fares.
Calculating the individual prices of a bat and a ball when the total cost of two different combinations of bats and balls is known.

Frequently Asked Questions

Why do we add or subtract equations in the elimination method?
We add or subtract the equations to cancel out the variable that has equal coefficients, reducing the system to a single linear equation in one variable which is easy to solve.
What does it mean if both variables eliminate and leave a true statement like 0 = 0?
This indicates that the pair of linear equations has infinitely many solutions, meaning the two equations represent coincident lines.

Keep Learning

Algebraic Solution MethodSubstitution MethodPair of Linear Equations