Solve the following pair of equations by substitution method: $7x - 15y = 2$ (1) and $x + 2y = 3$ (2).

Step 1: Express one variable in terms of the other

From equation (2), we can easily express $x$ in terms of $y$. This is the first step in the substitution method, as outlined in the NCERT textbook. We move the $2y$ term to the right side of the equation.

Step 2: Substitute the expression into the other equation

Now, we substitute the expression for $x$ ($3 - 2y$) from the first step into equation (1). This will give us a linear equation in a single variable, $y$, which we can then solve.

Step 3: Simplify and solve for y

We distribute the 7, combine like terms, and then isolate $y$. We subtract 21 from both sides and then divide by -29 to find the value of $y$.

Step 4: Substitute the value of y back into the expression for x

Now that we have the value of $y$, we substitute it back into the expression for $x$ we found in the first step. This allows us to calculate the value of $x$. We perform the multiplication and then find a common denominator to subtract the fractions.

Step 5: Verify the solution

We check if the calculated values of $x$ and $y$ satisfy both original equations. By plugging in $x = \frac{49}{29}$ and $y = \frac{19}{29}$ into equations (1) and (2), we confirm that both equations hold true, validating our solution.

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