Samacheer Kalvi 9th Maths Guide Chapter 3 Algebra Ex 3.10

Students can download Maths Chapter 3 Algebra Ex 3.10 Questions and Answers, Notes, Samacheer Kalvi 9th Maths Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams.

Tamilnadu Samacheer Kalvi 9th Maths Solutions Chapter 3 Algebra Ex 3.10

Question 1.
Draw the graph for the following:
(i) y = 2x
Solution:
When x = -2, y = 2 (-2) = -4
When x = 0, y = 2 (0) = 0
When x = 2, y = 2 (2) = 4
When x = 3, y = 2 (3) = 6
Samacheer Kalvi 9th Maths Guide Chapter 3 Algebra Ex 3.10 1
Plot the points (-2, -4) (0, 0) (2, 4) and (3, 6) in the graph sheet we get a straight line.
Samacheer Kalvi 9th Maths Guide Chapter 3 Algebra Ex 3.10 2

Samacheer Kalvi 9th Maths Guide Chapter 3 Algebra Ex 3.10

(ii) y = 4x – 1
Solution:
When x = – 1; y = 4 (-1) -1 ⇒ y = -5
When x = 0; y = 4 (0) – 1 = 0 – 1 ⇒ y = -1
When x = 2; y = 4 (2) -1 = 8 – 1 ⇒ y = l
Samacheer Kalvi 9th Maths Guide Chapter 3 Algebra Ex 3.10 3
Plot the points (-1, -5) (0, -1) and (2, 7) in the graph sheet we get a straight line. At the time of printing change the direction.
Samacheer Kalvi 9th Maths Guide Chapter 3 Algebra Ex 3.10 4

Samacheer Kalvi 9th Maths Guide Chapter 3 Algebra Ex 3.10

(iii) y = (\(\frac{3}{2}\))x + 3
Solution:
When x = -2;
y = \(\frac{3}{2}\)(-2) + 3
y = -3 + 3 = 0
when x = 0;
y = \(\frac{3}{2}\)(0) + 3
y = 3
when x = 2;
y = \(\frac{3}{2}\)(2) + 3
y = 3 + 3
= 6
Samacheer Kalvi 9th Maths Guide Chapter 3 Algebra Ex 3.10 5
Samacheer Kalvi 9th Maths Guide Chapter 3 Algebra Ex 3.10 6
Plot the points (-2, 0) (0, 3) and (2, 6) in the graph sheet we get a straight line.

Samacheer Kalvi 9th Maths Guide Chapter 3 Algebra Ex 3.10

(iv) 3x + 2y = 14
Solution:
y = \(\frac{-3x+14}{2}\)
y = – \(\frac{3}{2}\)x + 7
when x = -2
y = –\(\frac{3}{2}\)(-2) + 7 = 10
when x = 0
y = –\(\frac{3}{2}\)(0) + 7 = 7
when x = 2
y = –\(\frac{3}{2}\)(2) + 7 = 4
Samacheer Kalvi 9th Maths Guide Chapter 3 Algebra Ex 3.10 7
Samacheer Kalvi 9th Maths Guide Chapter 3 Algebra Ex 3.10 8
Plot the points (-2, 10) (0, 7) and (2, 4) in the graph sheet we get a straight line.

Samacheer Kalvi 9th Maths Guide Chapter 3 Algebra Ex 3.10

Question 2.
Solve graphically (i) x + y = 7, x – y = 3
Solution:
x + y = 7
y = 7 – x
Samacheer Kalvi 9th Maths Guide Chapter 3 Algebra Ex 3.10 9
Plot the points (-2, 9), (0, 7) and (3, 4) in the graph sheet
x – y = 3
-y = -x + 3
y = x – 3
Samacheer Kalvi 9th Maths Guide Chapter 3 Algebra Ex 3.10 10
Plot the points (-2, -5), (0, -3) and (4, 1) in the same graph sheet.
Samacheer Kalvi 9th Maths Guide Chapter 3 Algebra Ex 3.10 11
The point of intersection is (5, 2) of lines (1) and (2).
The solution set is (5,2).

Samacheer Kalvi 9th Maths Guide Chapter 3 Algebra Ex 3.10

(ii) 3x + 2y = 4; 9x + 6y – 12 = 0
Solution:
2y = -3x + 4
y = \(\frac{-3x+4}{2}\)
= \(\frac{-3}{2}\)x + 2
Samacheer Kalvi 9th Maths Guide Chapter 3 Algebra Ex 3.10 12
Plot the points (-2, 5), (0, 2) and (2, -1) in the graph sheet
9x + 6y= 12 (÷3)
3x + 2y = 4
2y = \(\frac{-3x+4}{2}\)
= \(\frac{-3}{2}\)x + 2
Samacheer Kalvi 9th Maths Guide Chapter 3 Algebra Ex 3.10 13
Plot the points (-2, 5), (0, 2) and (2, -1) the same graph sheet
Samacheer Kalvi 9th Maths Guide Chapter 3 Algebra Ex 3.10 14
Here both the equations are identical, but in different form.
Their solution is same.
This equations have an infinite number of solution.

Samacheer Kalvi 9th Maths Guide Chapter 3 Algebra Ex 3.10

(iii) \(\frac{x}{2}\) + \(\frac{y}{4}\) = 1: \(\frac{x}{2}\) + \(\frac{y}{4}\) = 2
Solution:
\(\frac{x}{2}\) + \(\frac{y}{4}\) = 1
multiply by 4
2x + y = 4
y = -2x + 4
Samacheer Kalvi 9th Maths Guide Chapter 3 Algebra Ex 3.10 15
Plot the points (-3, 10), (-1, 6), (0, 4) and (2, 0) in the graph sheet
\(\frac{x}{2}\) + \(\frac{y}{4}\) = 2
multiply by 4
2x + y = 8
y = -2x + 8
Samacheer Kalvi 9th Maths Guide Chapter 3 Algebra Ex 3.10 16
Plot the points (-2, 12), (-1, 10), (0, 8) and (2, 4) in the same graph sheet.
Samacheer Kalvi 9th Maths Guide Chapter 3 Algebra Ex 3.10 17
The given two lines are parallel.
∴ They do not intersect a point.
∴ There is no solution.

Samacheer Kalvi 9th Maths Guide Chapter 3 Algebra Ex 3.10

(iv) x – y = 0; y + 3 = 0
Solution:
x – y = 0
-y = -x
y = x
Samacheer Kalvi 9th Maths Guide Chapter 3 Algebra Ex 3.10 18
Plot the points (-2, -2), (0, 0), (1, 1) and (3, 3) in the same graph sheet.
y + 3 = 0
y = -3
Samacheer Kalvi 9th Maths Guide Chapter 3 Algebra Ex 3.10 19
Plot the points (-2, -3), (0, -3), (1, -3) and (2, -3) in the same graph sheet.
Samacheer Kalvi 9th Maths Guide Chapter 3 Algebra Ex 3.10 20
The two lines l1 and l2 intersect at (-3, -3). The solution set is (-3, -3).

Samacheer Kalvi 9th Maths Guide Chapter 3 Algebra Ex 3.10

(v) y = 2x + 1; 3x – 6 = 0
Solution:
y = 2x + 1
Samacheer Kalvi 9th Maths Guide Chapter 3 Algebra Ex 3.10 21
Plot the points (-3, -5), (-1, -1), (0, 1) and (2, 5) in the graph sheet
3x – 6 = 0
y = -3x + 6
Samacheer Kalvi 9th Maths Guide Chapter 3 Algebra Ex 3.10 22
Plot the points (-2, 12), (-1, 9), (0, 6) and (2, 0) in the same graph sheet
Samacheer Kalvi 9th Maths Guide Chapter 3 Algebra Ex 3.10 23
The two lines l1 and l2 intersect at (1, 3).
∴ The solution set is (1, 3).

(vi) x = -3; y = 3
Solution:
x = -3
Samacheer Kalvi 9th Maths Guide Chapter 3 Algebra Ex 3.10 24
Plot the points (-3, -3), (-3, -2), (-3, 2) and (-3, 3) in the graph sheet
y = 3
Samacheer Kalvi 9th Maths Guide Chapter 3 Algebra Ex 3.10 25
Plot the points (-3, 3), (-1, 3), (0, 3) and (2, 3) in the same graph sheet
Samacheer Kalvi 9th Maths Guide Chapter 3 Algebra Ex 3.10 26
The two lines l1 and l2 intersect at (-3, 3)
∴ The solution set is (-3, 3)

Samacheer Kalvi 9th Maths Guide Chapter 3 Algebra Ex 3.10

Question 3.
Two cars are 100 miles apart. If they drive towards each other they will meet in 1 hour. If they drive in the same direction they will meet in 2 hours. Find their speed by using graphical method.
Solution:
Let the speed of the two cars be “x” and “y”.
By the given first condition
Samacheer Kalvi 9th Maths Guide Chapter 3 Algebra Ex 3.10 27
x+ y = 100 → (1)
(They travel in opposite direction)
By the given second condition.
\(\)\frac{100}{x-y}= 2 [time taken in 2 hours in the same direction]
2x – 2y = 100
x – y = 50 → (2)
x + y = 100
y = 100 – x
Samacheer Kalvi 9th Maths Guide Chapter 3 Algebra Ex 3.10 28
Plot the points (30, 70), (50, 50), (60, 40) and (70,30) in the graph sheet
x – y = 50
-y = -x + 50
y = x – 50
Samacheer Kalvi 9th Maths Guide Chapter 3 Algebra Ex 3.10 29
Plot the points (40, -10), (50, 0), (60, 10) and (70, 20) in the same graph sheet
Samacheer Kalvi 9th Maths Guide Chapter 3 Algebra Ex 3.10 30
The two cars intersect at (75, 25)
The speed of the first car 75 km/hr
The speed of the second car 25 km/hr

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