NCERT · Class 10 · Mathematics · Pair of Linear Equations in Two VariablesSolve the system of equations $2x + y = 5$ and $3x + 2y = 8$ using the elimination method.

Given equations:

1. $2x + y = 5$ --- (Equation 1)
2. $3x + 2y = 8$ --- (Equation 2) \nTo eliminate $y$, multiply Equation 1 by $2$: $$2 \times (2x + y) = 2 \times 5 \implies 4x + 2y = 10$$ --- (Equation 3) \nNow, subtract Equation 2 from Equation 3: $$(4x + 2y) - (3x + 2y) = 10 - 8$$ $$4x - 3x + 2y - 2y = 2 \implies x = 2$$ \nSubstitute $x = 2$ into Equation 1 to find $y$: $$2(2) + y = 5 \implies 4 + y = 5 \implies y = 1$$ \nHence, the required solution is $x = 2$ and $y = 1$.