Solve the following pair of equations by substitution method: 7x−15y=2 (1) and x+2y=3 (2).
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Step-by-Step Solution
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=2949 and y=2919 into equations (1) and (2), we confirm that both equations hold true, validating our solution.