MP Board · Class 10 · Mathematics · Pair of Linear Equations in Two VariablesExplain the method of elimination and substitution for solving a pair of linear equations in two variables. Provide a suitable example to illustrate your answer.

Method of Elimination\nThe method of elimination is a technique used to solve a pair of linear equations in two variables. It involves adding or subtracting the equations to eliminate one of the variables.

Step 1: Write the equations in the standard form\nax + by = c\ndx + ey = f

Step 2: Multiply the equations by necessary multiples such that the coefficients of y's in both equations are the same\na'x + b'y = c'\nd'x + e'y = f'

Step 3: Subtract the second equation from the first equation

(a' - d')x = c' - f'

Step 4: Solve for x\nx = (c' - f') / (a' - d')

Step 5: Substitute the value of x in one of the original equations to solve for y\nax + by = c\na((c' - f') / (a' - d')) + by = c

Example\nSolve the pair of linear equations: 2x + 3y = 7 and x - 2y = -3.

Step 1: Write the equations in the standard form

2x + 3y = 7\nx - 2y = -3

Step 2: Multiply the equations by necessary multiples such that the coefficients of y's in both equations are the same

2x + 3y = 7\nx - 2y = -3

Step 3: Subtract the second equation from the first equation

(2x + 3y) - (x - 2y) = 7 - (-3)\nx + 5y = 10

Step 4: Solve for x\nx = (10 - 5y) / 1\nx = 10 - 5y

Step 5: Substitute the value of x in one of the original equations to solve for y

2x + 3y = 7 2(10 - 5y) + 3y = 7 20 - 10y + 3y = 7 -7y = -13\ny = 13/7

Conclusion\nThe solution of the given pair of linear equations is x = 10 - 5y and y = 13/7.