Pair of Linear Equations in Two Variables · Class 10 · CBSE Mathematics

Solve the following pair of linear equations using the substitution method: 2x + y = 7 and 4x - 3y = 1.

Practice question from Pair of Linear Equations in Two Variables (Class 10 · CBSE Mathematics), with the correct answer and a step-by-step solution.

medium · Subjective · Q-1D9427

Solve the following pair of linear equations using the substitution method: $2x + y = 7$ and $4x - 3y = 1$ .

Answer: From the first equation, express

y

in terms of

x

y = 7 - 2x

. Substituting this into the second equation gives

4x - 3(7 - 2x) = 1

, which simplifies to

4x - 21 + 6x = 1

, or

10x = 22

, yielding

x = 2.2

\frac{11}{5}

. Substituting

x = \frac{11}{5}

back into

y = 7 - 2x

gives

y = 7 - \frac{22}{5} = \frac{13}{5}

. Thus, the solution is

x = \frac{11}{5}

and

y = \frac{13}{5}

Solution

Express $y$ from the first equation as $y = 7 - 2x$ and substitute it into the second equation. Solving the resulting linear equation in one variable gives $x = \frac{11}{5}$ . Substituting this value back yields $y = \frac{13}{5}$ .

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