Question

Solve graphically the pair of linear equations 3x - 4y + 3 = 0 and 3x + 4y- 21=0.Find the coordinates of vertices of triangular region formed by these lines and x-axis. Also calculate the area of this triangle.

Answer 1

A pair of  linear equations in two variables will be represented by two straight lines taken together.

For two lines in a plane following three possibilities can happen:

1.The two lines representing a pair of  linear equations will intersect at a point.
2. The two lines representing a pair of linear equations will not intersect or  they are parallel to each other.
3. The two lines representing a parallel equations in two variables will be coincident they overlap each other.

•In order to represent the pair of  linear equation graphically we need two points on the line representing each equation.
• Prepare the proper table of at least 2 solutions for both the equations.
•Draw the graph of both the question on the same graph paper with same scale of  representation.

SOLUTION:

Given pair of Linear Equations are:
3x - 4y +3 =0  ……………….(1)
3x + 4y - 21 = 0 …………….(2)

Put x= 3 in eq 1
3x - 4y +3 =0
3×3  - 4y +3= 0
9 - 4y = - 3
9 +3 = 4y
12 = 4y
y = 12/4= 3

A(3, 3)

Put y= 0 in eq 1
3x - 4 × 0 = -3
3x = -3
x =- 3/3 = -1

B(-1,0)

Put x= 3 in eq 2
3x + 4y -21 =0
3×3  + 4y = 21
9 + 4y = 21
4y = 21 -9
4y = 12
y = 12/4= 3

A(3, 3)

Put y= 0 in eq 2
3x + 4×0= 21
3x + 0  = 21
3x = 21
x = 21/3
x = 7
x = 2

C(7,0)

TABLE AND GRAPH are on the ATTACHMENT.

The coordinates of the vertices of ∆ABC are A(3, 3) , B(-1,0) & C(7,0)

Area of ∆ ABC = ½ (base × height)
Area of ∆ ABC = ½ (AM × BC)
[From the graph , AM = 3 , BC = 8]

Area of ∆ ABC = ½ (3 × 8) = 24/2 = 12 sq units.

HOPE THIS WILL HELP YOU...

Answer 2

Answer:

Step-by-step explanation:hope this can surely help you...