Is it true to say that the pair of equations -x + 2y + 2 = 0 and (1/2)x - (1/4)y - 1 = 0 has a unique solution? Justify your answer.
Solution:
Given, the pair of equations:
-x + 2y + 2 = 0
(1/2)x - (1/4)y - 1 = 0
We have to determine whether the pair of equations has a unique solution or not.
We know that,
For a pair of linear equations in two variables be a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0,
If \(\frac{a_{1}}{a_{2}}\neq \frac{b_{1}}{b_{2}}\), then the graph will be a pair of lines intersecting at a unique point, which is the solution of the pair of equations.
Here, a₁ = -1, b₁ = 2, c₁ = 2
a₂ = 1/2, b₂ = -1/4, c₂ = -1
So, a₁/a₂ = -1/(1/2) = -2
b₁/b₂ = 2/(-1/4) = -8
\(\frac{a_{1}}{a_{2}}\neq \frac{b_{1}}{b_{2}}\)
Therefore, the pair of equations has a unique solution.
✦ Try This: Determine if the pair of equations 2x - y = 0 and 3x + 7y = 0 has a unique solution or not.
Given, the pair of equations are
2x - y = 0
3x + 7y = 0
We have to determine whether the pair of equations has a unique solution or not.
Here, a₁ = 2, b₁ = -1
a₂ = 3, b₂ = 7
So, a₁/a₂ = 2/3
b₁/b₂ = -1/7
\(\frac{a_{1}}{a_{2}}\neq \frac{b_{1}}{b_{2}}\)
Therefore, the pair of equations has a unique solution
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 3
NCERT Exemplar Class 10 Maths Exercise 3.2 Sample Problem 1
Is it true to say that the pair of equations -x + 2y + 2 = 0 and (1/2)x - (1/4)y - 1 = 0 has a unique solution? Justify your answer
Summary:
The pair of equations -x + 2y + 2 = 0 and (1/2)x - (1/4)y - 1 = 0 has a unique solution
☛ Related Questions:
visual curriculum