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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 Summary: The pair of equations -x + 2y + 2 = 0 and (1/2)x - (1/4)y - 1 = 0 has a unique solution ☛ Related Questions: |