MathsCBSE Class 10 · Basic · Board exam 2024, set 430/3/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Basic 2024: question 35(a)

Set in the CBSE Class 10 board exam of 2024, paper 430/3/1, section D, question 35(a), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q35(a) · 5 marks · Long answerPair of Linear Equations in Two Variables

Using graphical method, solve the following pair of equations: $x + 2 y = 8$ and $3 x -2 y = 12$

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 430/3/1.

Hints

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

Hint 1

For each equation, find at least two points by putting $x = 0$ and then $y = 0$ .

Hint 2

Draw both lines on the same axes and look for the point they share.

Hint 3

The coordinates of the point where the lines cross give the solution; check them in both equations.

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.

**Table for $x + 2 y = 8$ **, i.e. $y = \frac{8 - x}{2}$ :
$x$ 0 8 2
$y$ 4 0 3
1 mark
**Table for $3 x - 2 y = 12$ **, i.e. $y = \frac{3 x - 12}{2}$ :
$x$ 0 4 2
$y$ −6 0 −3
1 mark
On graph paper, plot $(0, 4)$ , $(8, 0)$ and $(2, 3)$ . Join them to get the line $x + 2 y = 8$ .
1 mark
On the same axes, plot $(0, - 6)$ , $(4, 0)$ and $(2, - 3)$ . Join them to get the line $3 x - 2 y = 12$ .
1 mark
The two lines intersect at the point $(5, 1.5)$ .
Check: $5 + 2 (1.5) = 8$ ✓ and $3 (5) - 2 (1.5) = 12$ ✓.
Hence the solution is $x = 5$ , $y = 1.5$ .
1 mark

$x$	0	8	2
$y$	4	0	3

$x$	0	4	2
$y$	−6	0	−3

Answer: x = 5, y = 1.5 (the lines meet at (5, 1.5))

Where the marks are

Correct table of values for $x + 2 y = 8$ (1 mark)
Correct table of values for $3 x - 2 y = 12$ (1 mark)
Correct graph of $x + 2 y = 8$ (1 mark)
Correct graph of $3 x - 2 y = 12$ (1 mark)
Reads the intersection point and states $x = 5$ , $y = 1.5$ (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 430/3/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2024: question 35(a)

Hints

Step-by-step solution

Revise the chapter

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