CBSE · Class 10 · Mathematics · Pair of Linear Equations in Two VariablesSolve the following pair of linear equations in two variables: 3x + 4y = 8 and 2x - 3y = 7.
Step-by-Step Solution
Method of Substitution
Step 1: Solve the first equation for x
3x + 4y = 8 3x = 8 - 4y\nx = (8 - 4y) / 3
Step 2: Substitute the value of x in the second equation
2((8 - 4y) / 3) - 3y = 7 (16 - 8y) / 3 - 3y = 7 (16 - 8y) - 9y = 21 16 - 17y = 21 -17y = 5\ny = -5/17
Step 3: Substitute the value of y in the first equation
3x + 4(-5/17) = 8 3x - 20/17 = 8 3x = 8 + 20/17 3x = (136 + 20) / 17 3x = 156/17\nx = 156/51\nx = 52/17
Conclusion\nThe solution of the given pair of linear equations is x = 52/17 and y = -5/17.
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