**Concise Class-9 Graphical Solution** of Simultaneous Linear Equations Chapter-27 . We provide step by step Solutions of Exercise / lesson-27 **Graphical Solution** for ICSE **Class-9 Concise** Selina Mathematics by R. K. Bansal.

Our Solutions contain all type Questions with Exe-27 A, Exe-27 B, to develop skill and confidence. Visit official Website **CISCE** for detail information about ICSE Board Class-9 Mathematics

**Concise Class-9 Graphical Solution** of Simultaneous Linear Equations Chapter-27

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Let the system of pair of linear equations be

a_{1}x + b_{1}y = c_{1} ….(1)

a_{2}x + b_{2}y = c_{2} ….(2)

We know that given two lines in a plane, only one of the following three possibilities can happen –

(i) The two lines will intersect at one point.

(ii) The two lines will not intersect, however far they are extended, i.e., they are parallel.

(iii) The two lines are coincident lines.

#### How to solve a pair of simultaneous equations graphically?

In order to solve a pair of simultaneous equations graphically, we first draw the graph of the two equations simultaneously. We get two straight lines intersecting each other at a common point. This common point intersection of two lines gives the solution of the pair of simultaneous equations.

**Exe-27 A,** Selina Concise Class-9 Graphical Solution of Simultaneous Linear Equations

**Question. 1**

Draw the graph for the equation, given below :

(i) x = 5

(ii) x +5 =0

(iii) y = 7

(iv) y+7=0

(v) 2x + 3y =0

(vi) 3x + 2y = 6

(vii) x-5y+4=0

(viii) 5x + y +5=0

**Answer 1:**

(i)

The graph x= 5 in the following figure is a straight line AB which is parallel to y axis at a distance of 5 units from it.

(ii)

x+5=0

x = -5

The graph x= -5 in the following figure is a straight line AB which is parallel to y axis at a distance of 5 units from it in the negative x direction.

(iii)

The graph y = 7 in the following figure is a straight line AB which is parallel to x axis at a distance of 7 units from it.

(iv)

y + 7 = 0

y = -7

The graph y = -7 in the following figure is a straight line AB which is parallel to x axis at a distance of 7 units from it in the negative y direction.

**Question. 2**

Draw the graph for the equation given below; hence find the co-ordinates of the points where the graph is drawn meets the co-ordinates axes:

(i) x/3 + y/5 =1

(ii) (2x + 15) /3 = y – 1

**Answer 2:**

From the figure it is clear that, the graph meets the coordinate axes at (-9, 0) and (0, 6)

**Question. 3**

Draw the graph of the straight line given by the equation 4x – 3y + 36 = 0

Calculate the area of the triangle formed by the line drawn and the co-ordinate axes.

**Answer 3:**

**Question. 4**

Draw the graph of the equation 2x – 3y – 5 = 0

From the graph, find:

(i) x_{1}, the value of x, when y = 7

(ii) x_{2}, the value of x, when y = – 5.

**Answer 4:**

**Question. 5**

Draw the graph of the equation

4x + 3y + 6 = 0

From the graph, find :

(i) y_{1}, the value of y, when x = 12.

(ii) y_{2}, the value of y, when x = – 6.

**Answer 5:**

**Question. 6**

Use the table given below to draw the graph.

X | – 5 | – 1 | 3 | b | 13 |

Y | – 2 | a | 2 | 5 | 7 |

From your graph, find the values of ‘a’ and ‘b’.

State a linear relationship between the variables x and y.

**Answer 6:**

**Question. 7**

Draw the graph obtained from the table below:

X | a | 3 | – 5 | 5 | c | – 1 |

Y | – 1 | 2 | b | 3 | 4 | 0 |

Use the graph to find the values of a, b and c. State a linear relation between the variables x and y.

**Answer 7:**

**Question. 8**

A straight line passes through the points (2, 4) and (5, – 2). Taking 1 cm = 1 unit; mark these points on a graph paper and draw the straight line through these points. If points (m, – 4) and (3, n) lie on the line drawn; find the values of m and n.

**Answer 8:**

**Question. 9**

Draw the graph (straight line) given by equation x – 3y = 18. If the straight line is drawn passes through the points (m, – 5) and (6, n); find the values of m and n

**Answer 9:**

**Question. 10**

Use the graphical method to find the value of k, if:

(i) (k, -3) lies on the straight line 2x + 3y = 1

(ii) (5, k – 2) lies on the straight line x – 2y + 1 = 0

**Answer 10:**

**Exe-27 B,** Concise Selina Class-9 Graphical Solution of Simultaneous Linear Equations

**Question. 1**

Solve, graphically, the following pairs of equation :

(i) x – 5 = 0 , y + 4 = 0

(ii) 2x + y = 23 , 4x – y = 19

(iii) 3x + 7y = 27, 8 – y = 5x/2

(iv)…………….

**Answer 1:**

**Question. 2**

Solve graphically the simultaneous equations given below. Take the scale as 2 cm = 1 unit on both the axes.

x – 2y – 4 = 0

2x + y = 3

**Answer 2:**

**Question. 3**

Use graph paper for this question. Draw the graph of 2x – y – 1 = 0 and 2x + y = 9 on the same axes. Use 2 cm = 1 unit on both axes and plot only 3 points per line. Write down the coordinates of the point of intersection of the two lines.

**Answer 3:**

**Question. 4**

Use graph paper for this question. Take 2 cm = 2 units on x-axis and 2 cm = 1 unit on y-axis.

Solve graphically the following equation :

3x + 5y = 12; 3x – 5y + 18 = 0 (Plot only three points per line)

**Answer 4:**

**Question. 5**

Use graph paper for this question. Take 2 cm = 1 unit on both the axes.

(i) Draw the graphs of x + y + 3 = 0 and 3x – 2y + 4 = 0. Plot only three points per line.

(ii) Write down the coordinates of the point of intersection of the lines.

(iii) Measure and record the distance of the point of intersection of the lines from the origin in cm.

**Answer 5:**

**Question. 6**

The sides of a triangle are given by the equations y – 2 = 0; y + 1 = 3 (x – 2) and x + 2y = 0.

Find, graphically :

(i) the area of a triangle;

(ii) the coordinates of the vertices of the triangle.

**Answer 6:**

**Question. 7**

By drawing a graph for each of the equations 3x + y + 5 = 0; 3y – x = 5 and 2x + 5y = 1 on the same graph paper; show that the lines given by these equations are concurrent (i.e. they pass through the same point). Take 2 cm = 1 unit on both the axes.

**Answer 7:**

**Question. 8**

Using a scale of 1 cm to 1 unit for both the axes, draw the graphs of the following equations: 6y = 5x + 10, y = 5x – 15.

From the graph find :

(i) the coordinates of the point where the two lines intersect;

(ii) the area of the triangle between the lines and the x-axis.

**Answer 8:**

**Question. 9**

The cost of manufacturing x articles is Rs. (50 + 3x). The selling price of x articles is Rs. 4x.

On a graph sheet, with the same axes, and taking suitable scales draw two graphs, first for the cost of manufacturing against no. of articles and the second for the selling price against the number of articles.

Use your graph to determine:

(i). No. of articles to be manufactured and sold to break even (no profit and no loss).

(ii). The profit or loss made when (a) 30 (b) 60 articles are manufactured and sold.

**Answer 9:**

**Question. 10**

Find graphically, the vertices of the triangle whose sides have the equations 2y – x = 8; 5y – x = 14 and y – 2x = 1 respectively. Take 1 cm = 1 unit on both the axes.

**Answer 10:**

**Question. 11**

Using the same axes of co-ordinates and the same unit, solve graphically :

x + y = 0 and 3x – 2y = 10.

(Take at least 3 points for each line drawn).

**Answer 11:**

**Question. 12**

Solve graphically, the following equations.

x + 2y = 4; 3x – 2y = 4.

Take 2 cm = 1 unit on each axis.

Also, find the area of the triangle formed by the lines and the x-axis.

**Answer 12:**

**Question. 13**

Use the graphical method to find the value of ‘x’ for which the expressions (3x+2)/2 and 3x/4 – 2

**Answer 13:**

**Question. 14**

The course of an enemy submarine, as plotted on rectangular co-ordinate axes, gives the equation 2x + 3y = 4. On the same axes, a destroyer’s course is indicated by the graph x – y = 7. Use the graphical method to find the point at which the paths of the submarine and the destroyer intersect?

**Answer 14:**

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