Selina solutions for कन्साइस मैथमैटिक्स [अंग्रेजी] कक्षा ९ आईसीएसई chapter 24 - Graphical Solution [Solution of Simultaneous Linear Equations, Graphically] [Latest edition]

Point (k, 2) lies on the line x − 4y = 2; the value of k is ______.

The line y = mx − 8 passes through the point (5, 2); the value of m is ______.

The line 5x − 2y − 10 = 0 intersects x-axis at point P. The co-ordinates of point P are ______.

The line 5x − 4y − 20 = 0 intersects y-axis at point A. The co-ordinates of point A are ______.

The point (0, 0) lies on ______.

Draw the graph for the equation, given below :
x = 5

Draw the graph for the equation, given below :
x + 5 = 0

Draw the graph for the equation, given below :
y = 7

Draw the graph for the equation, given below :
y + 7 = 0

Draw the graph for the equation, given below :
2x + 3y = 0

Draw the graph for the equation, given below:
3x + 2y = 6

Draw the graph for the equation, given below :
x - 5y + 4 = 0

Draw the graph for the equation, given below :
5x + y + 5 = 0

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:
`(1)/(3) x +(1)/(5) y = 1`.

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:
`(2x + 15)/(3) = y - 1`

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.

Draw the graph of the equation 2x - 3y - 5 = 0
From the graph, find:
(i) x₁, the value of x, when y = 7
(ii) x₂, the value of x, when y = - 5.

Draw the graph of the equation
4x + 3y + 6 = 0
From the graph, find :
(i) y₁, the value of y, when x = 12.
(ii) y₂, the value of y, when x = - 6.

Use the table given below to draw the graph.

From your graph, find the values of 'a' and 'b'.
State a linear relationship between the variables x and y.

Draw the graph obtained from the table below:

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

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.

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.

The point of intersection of lines x = 8 and y − 8 = 0 is ______.

For line y = 20 + 2x, if x = 20, the value of y is ______.

A point that lies on the line 2x − 3y = 4 can be taken as ______.

The line x + 5 = 0 ______.

The lines y − 2 = 0 and 2x + 3y = 12 cut each other at point ______.

Solve, graphically, the following pairs of equation :
x - 5 = 0 
y + 4 = 0

Solve, graphically, the following pairs of equation :
2x + y = 23
4x - y = 19

Solve, graphically, the following pairs of equation :
3x + 7y = 27
8 - y = `(5)/(2)x`

Solve, graphically, the following pairs of equations :
`(x + 1)/(4) = (2)/(3)(1 - 2y)`

`(2 + 5y)/(3) = x/(7) -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

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.

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)

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

1. Draw the graphs of x + y + 3 = 0 and 3x - 2y + 4 = 0. Plot only three points per line.
2. Write down the coordinates of the point of intersection of the lines.
3. Measure and record the distance of the point of intersection of the lines from the origin in cm.

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.

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.

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.

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

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

For the line 2x − y = 7 and for x = 3 the value of y is ______.

The line x + 3y + 2 = 0 passes through the point (4, k); then the value of k is ______.

Lines x − 5 = 0 and y + 3 = 0 intersect each other at point ______.

For the line 4x − 7y + 6 = 0 if x = 2; the value of y is ______.

Statement (1): The graph of 2x − 5 = 0 is a line parallel to y-axis.

Statement (2): When the equations of lines are of the form x = ± k (a constant), the lines are parallel to y-axis.

Statement (1): The lines of the form ax ± by = 0 always pass through the origin.

Statement (2): On substituting x = 0 and y = 0; we get a × 0 ± b × 0 = 0.

Assertion (A): y + 5 = 0 is the equation of the line parallel to x-axis and at a distance of 5 unit in the negative direction from it.

Reason (R): For all the points on the line y = a (a constant), the value of abscissa is a.

Assertion (A): For the line 3x + 4y = 7, the abscissa is `- 3/4`.

Reason (R): For abscissa of a point, y = 0 and 3x + 4y = 7 ⇒ `x = 7/3`.

Find the distance of point (8, −4) from y-axis.

Three vertices of parallelogram ABCD are A(−5, −1), B(3, −1) and C(1, −6). Use graphical method to find the co-ordinates of fourth vertex D.

In the given figure, ABC is an equilateral triangle. Find the co-ordinates of A.

Draw the graph of 3x + 2y = 6. Use the graph drawn to find the area of triangle formed by the line drawn and the co-ordinate axes.

Use the graphical method to find the value of k, if:
(k, -3) lies on the straight line 2x + 3y = 1

Use the graphical method to find the value of k, if:
(5, k - 2) lies on the straight line x - 2y + 1 = 0

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.

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).

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.

Use the graphical method to find the value of 'x' for which the expressions `(3x + 2)/(2) and (3)/(4)x - 2`

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?

An equation which can be put in the form ax + by + c = 0 is called a linear equation, where:

1. x and y are variables.
2. a, b and c are real numbers and
3. a and b are both not zero.

On drawing a graph for the two linear equations on the same plane, it is seen that only one of the following three possibilities can happen:

1. the two lines intersect at one point.
   
2. the two lines do not intersect (i.e. the lines are parallel to each other)
   
3. the two lines coincide (i.e. the lines have infinite number of solutions).
   

On comparing the ratios \[\frac{a_1}{a_2}, \frac{b_1}{b_2}\text{ and }\frac{c_1}{c_2}\], find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident.

1. 7x − 5y + 10 = 0
   6x + 2y − 15 = 0
2. 5x + 2y + 8
   15x + 6y + 24 = 0
3. 4x − 8y + 9 = 0
   2x − 4y + 7 = 0
4. x − 2y = 0
   3x − 4y − 20 = 0
5. 2x + 3y − 9 = 0
   4x + 6y − 18 = 0
6. x + 2y − 4 = 0
   2x + 4y − 12 = 0