MathsCBSE Class 10 · Basic · Board exam 2024, set 430/1/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2024: question 22(B)

Set in the CBSE Class 10 board exam of 2024, paper 430/1/1, section B, question 22(B), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q22(B) · 2 marks · Very short answerPair of Linear Equations in Two Variables

Check whether the point $(- 4, 3)$ lies on both the lines represented by the linear equations $x + y + 1 = 0$ and $x - y = 1$ .

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 430/1/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

A point lies on a line if its coordinates satisfy the line's equation.

Hint 2

Substitute $x = - 4$ , $y = 3$ in each equation separately and compare LHS with RHS.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

For $x + y + 1 = 0$ : put $x = - 4, y = 3$ : LHS $= - 4 + 3 + 1 = 0 =$ RHS. So $(- 4, 3)$ lies on this line.
1 mark
For $x - y = 1$ : LHS $= - 4 - 3 = - 7 \neq = 1$ . So $(- 4, 3)$ does not lie on this line. Hence the point does not lie on both lines.
1 mark

Answer: $(- 4, 3)$ lies on $x + y + 1 = 0$ but not on $x - y = 1$ ; so it does not lie on both lines.

Where the marks are

Substitutes in $x + y + 1 = 0$ and shows it is satisfied (1 mark)
Substitutes in $x - y = 1$ , shows it is not satisfied and concludes (1 mark)

Revise the chapter

Chapter: Pair of Linear Equations in Two Variables (notes, formulas, where marks are lost and every past question)
Topic: Graphical Method of Solving Linear Equations

Practise this chapterBoard-style questions from Pair of Linear Equations in Two Variables, one at a time, marked against the answer key and marking points.Back to the full paper2024 board paper, set 430/1/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2024: question 22(B)

Hints

Step-by-step solution

Revise the chapter

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