Write an equation of a line passing through the point representing the solution of the pair of linear equations x + y = 2 and 2x - y = 1. How many such lines can we find
Solution:
From the above question, we have the linear equations as,
x + y - 2 = 0----------(1)
2x - y - 1 = 0---------(2)
Comparing with the general form of straight line ax + by + c = 0, we get,
aₗ = 1, bₗ = 1 cₗ = -2
a₂ = 2, b₂ = -1 c₂ = -1
aₗ/a₂ = 1/2;
bₗ/ b₂ = -1;
cₗ/c₂ = 2.
aₗ/a₂ ≠ bₗ/ b₂.
In this, both lines intersect at a point.
Hence, the pair of equations has a unique solution.
Therefore, these equations are consistent.
Now, x + y = 2
y = 2 - x.
|
x |
0 |
2 |
1 |
|---|---|---|---|
|
y |
2 |
0 |
1 |
And 2x - y - 1 = 0
y = 2x - 1
|
x |
0 |
1/2 |
1 |
|---|---|---|---|
|
y |
-1 |
0 |
1 |
The given lines intersect at E(1,1).
Therefore, infinite lines can pass through the intersection point of linear equations x + y = 2 and 2x - y = 1 i.e., E( 1, 1) like y = x, 2x + y = 3, x + 2y = 3 and so on.
Therefore, infinite lines can pass through the intersection point of linear equations x + y = 2 and 2x - y = 1.
✦ Try This: Write an equation of a line passing through the point representing the solution of the pair of linear equations x+y = 1 and 2x-y = 2. How many such lines can we find?
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 3
NCERT Exemplar Class 10 Maths Exercise 3.3 Problem 13
Write an equation of a line passing through the point representing the solution of the pair of linear equations x + y = 2 and 2x - y = 1. How many such lines can we find?
Summary:
An equation of a line passing through the point representing the solution of the pair of linear equations x+y = 2 and 2x-y = 1 is y = x, 2x + y = 3, x + 2y = 3 and so on.
☛ Related Questions:
- The angles of a triangle are x, y and 40°. The difference between the two angles x and y is 30°. Fin . . . .
- Two years ago, Salim was thrice as old as his daughter and six years later, he will be four years ol . . . .
- The age of the father is twice the sum of the ages of his two children. After 20 years, his age will . . . .