MP Board · Class 10 · Mathematics · Pair of Linear Equations in Two VariablesIf $x = a$ and $y = b$ is the solution of the linear equations $x - y = 2$ and $x + y = 4$, then find the values of $a$ and $b$.

The given system of equations is:

1. $x - y = 2$ --- (Equation 1)
2. $x + y = 4$ --- (Equation 2) \nSince $x = a$ and $y = b$ is the solution, substitute $x = a$ and $y = b$ into both equations:

• $a - b = 2$ --- (Equation 3)
• $a + b = 4$ --- (Equation 4) \nAdding Equation 3 and Equation 4: $$(a - b) + (a + b) = 2 + 4 \implies 2a = 6 \implies a = 3$$ \nNow, substitute $a = 3$ into Equation 4: $$3 + b = 4 \implies b = 4 - 3 \implies b = 1$$ \nHence, the required values are $a = 3$ and $b = 1$.