We have x = y
Thus, we have following table :

We have, y = 2x
Thus, we have following table :

We have x + y = 6
⇒ x = 6 – y

Fig. 3.20.

Thus, we have following table :
Co-ordinates of the vertices are (0, 0), (2, 4), (3, 3).

We have
x + y = 5
⇒ x = 5 – y
Thus, we have the following table :

We have 3x – y = 3
⇒ y = 3x – 3
Thus, we have following table :

Fig. 3.22.

When we plot the graph of the given equations, we find that both the lines intersect at the point (2, 3), therefore, x = 3, y = 2 is the solution of the given system of equation.

Let the cost of 1 bat be Rs. x and cost of I ball be Rs.y
Case I. Cost of 3 bats = 3x
Cost of 6 balls = 6y
According to question,
3x + 6y = 3900
Case II. Cost of I bat = x
Cost of 3 more balls = 3y
According to question,
x + 3y = 1300
So, algebraically representation be
3x + 6y = 3900
x + 3y = 1300
Graphical representation :
We have, 3x + 6y = 3900
⇒ 3(x + 2y) = 3900
⇒ x + 2y = 1300
⇒ a = 1300 – 2y
Thus, we have following table :

We have, x + 3y = 1300
⇒ x = 1300 – 3y
Thus, we have following table :
When we plot the graph of equations, we find that both the lines intersect at the point (1300. 0). Therefore, a = 1300, y = 0 is the solution of the given system of equations.

Draw the graphs of the equations :
x – y = 1
and 2x + y = 8
Determine the vertices of the triangle formed by these lines and x-axis.

We have :
x – y = 1
⇒ x = y + 1
Thus, we have following table :
Thus, we have following table :

Fig. 3.21.

When we plot the graph of the given equations, we find that both the lines intersect at the point (3, 2), therefore x = 3, y = 2 is the solution of the given system of equations.

Vertices of triangle are A(3, 2), 13(1, 0), C(4, 0).

Represent the following system of linear equations graphically from the graph find the points where the lines intersect y-axis.

3x + y – 5 = 0, 2x – y – 5 = 0

We have,
3x + y – 5 = 0
⇒ y = 5 – 3x
Thus we have following table :

We have, 2x – y – 5 = 0
⇒ y = 2x – 5
Thus, we have following table :

Fig. 3.19.
When we plot the graph of the given equation, we find that both the lines intersect at the point (-1, 2), therefore x = -1, y = 2 is the solution of the given system of equations.
From the graph we observe that lines intersect y-axis at (-5, 0) and (5,0)

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