x + y = 3, 3x + 3y = 9, find whether the following pair of equations are consistent or not. If consistent, solve them
Solution:
From the above question, we have the equation as,
x + y = 3
x + y- 3 = 0-----------(1)
3x + 3y = 9
3x + 3y - 9 = 0-------(2)
Comparing with the general form of straight line ax + by + c = 0, we get,
aₗ = 1, bₗ = 1, cₗ = -3
a₂ = 3, b₂ = 3, c₂ = -9 .
aₗ/a₂ = 1/3;
bₗ/b₂ = 1/3;
cₗ/c₂ = 1/3.
aₗ/a₂ = bₗ/b₂ = cₗ/c₂.
Hence, the given pair of lines is coincident.
Hence, these lines have infinitely many solutions.
Therefore, the given pair of linear equations is consistent.
Now, x + y = 3 ⇒ y = 3 - x
|
x |
0 |
3 |
2 |
|---|---|---|---|
|
y |
3 |
0 |
1 |
3x + 3y = 9
3y = 9 - 3x
y = (9 - 3x)/ 3
|
x |
0 |
1 |
3 |
|---|---|---|---|
|
y |
3 |
2 |
0 |
Plotting the points we get the graph of lines.
Therefore, the given pairs are coincident and consistent.
✦ Try This: By the graphical method, find whether the following pair of equations are consistent or not. If consistent, solve them. x + y = 4., 3x + 3y = 8
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 3
NCERT Exemplar Class 10 Maths Exercise 3.3 Problem 11 (iii)
x + y = 3, 3x + 3y = 9, find whether the following pair of equations are consistent or not. If consistent, solve them
Summary:
By the graphical method, the given pairs of equations x + y = 3 and 3x + 3y = 9 are coincident and consistent
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