Graphically, solve the following pair of equations: 2x + y = 6; 2x - y + 2 = 0. Find the ratio of the areas of the two triangles formed by the lines representing these equations with the x-axis and the lines with the y-axis
Solution:
From the above question, we have the equation as,
2x + y = 6
2x - y + 2 = 0.
Table for equation 2x + y = 6.
|
x |
0 |
3 |
|---|---|---|
|
y |
6 |
0 |
Table for equation 2x - y + 2 = 0
|
x |
0 |
-1 |
|---|---|---|
|
y |
2 |
0 |
The pair of equations intersect graphically at point E(1, 4),
x = 1
y = 4
Let A₁ represent the area of ∆ACE
lET A₂ represents the area of ∆BDE.
A₁ = Area of ∆ACE = 1/2 x AC x PE.
Area of ∆ACE = 1/2 x 4 x 4
Area of ∆ACE = 8.
A₂ = Area of ∆ BDE = 1/2 x BD x QE
Area of ∆ BDE = 1/2 x 4 x 1
Area of ∆ BDE = 2.
Therefore, the required ratio = A₁ : A₂ = 8 : 2 = 4 : 1
✦ Try This: Graphically, solve the following pair of equations: 2x + y = 4; 2x - y + 2 = 0. Find the ratio of the areas of the two triangles formed by the lines representing these equations with the x-axis and the lines with the y-axis
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 3
NCERT Exemplar Class 10 Maths Exercise 3.4 Problem 1
Graphically, solve the following pair of equations: 2x + y = 6; 2x - y + 2 = 0. Find the ratio of the areas of the two triangles formed by the lines representing these equations with the x-axis and the lines with the y-axis
Summary:
Graphically, solving the following pair of equations: 2x + y = 6; 2x - y + 2 = 0. The ratio of the areas of the two triangles formed by the lines representing these equations with the x-axis and the lines with the y-axis is 4 : 1.
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