CBSE · Class 10 · Mathematics · Pair of Linear Equations in Two VariablesSolve the pair of linear equations $2x + 3y = 11$ and $2x - 4y = -24$ by substitution method. Hence, find the value of '$m$' for which $y = mx + 3$.

Given equations are:

1. $2x + 3y = 11$
2. $2x - 4y = -24$

Step 1: From equation (2), express $x$ in terms of $y$: $$2x = 4y - 24$$ $$x = 2y - 12 \quad \text{--- (3)}$$

Step 2: Substitute the value of $x$ from (3) into equation (1): $$2(2y - 12) + 3y = 11$$ $$4y - 24 + 3y = 11$$ $$7y - 24 = 11$$ $$7y = 35$$ $$y = 5$$

Step 3: Substitute $y = 5$ in equation (3): $$x = 2(5) - 12$$ $$x = 10 - 12 = -2$$ \nSo, the solution is $x = -2$ and $y = 5$.

Step 4: Find the value of $m$ using $y = mx + 3$: $$5 = m(-2) + 3$$ $$5 - 3 = -2m$$ $$2 = -2m$$ $$m = -1$$

Final Answer: $x = -2$, $y = 5$, and $m = -1$.