Which of the following pairs of linear equations are consistent/inconsistent ? If consistent, obtain the solution graphically :
2x + y - 6 = 0, 4x - 2y - 4 = 0

Question

Which of the following pairs of linear equations are consistent/inconsistent ? If consistent, obtain the solution graphically : 2x + y - 6 = 0, 4x - 2y - 4 = 0

KnowledgeBoat · Accepted Answer

Given, Equations : ⇒ 2x + y - 6 = 0, 4x - 2y - 4 = 0 Comparing equations 2x + y - 6 = 0 and 4x - 2y - 4 = 0 with a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 respectively, we get : a₁ = 2, b₁ = 1, c₁ = -6, a₂ = 4, b₂ = -2 and c₂ = -4. Since, ≠ . Hence, pair of lines are consistent. 1st equation : 2x + y - 6 = 0 ⇒ y = 6 - 2x ..........(1) 2nd equation : 4x - 2y - 4 = 0 ⇒ 2y = 4x - 4 ⇒ 2y = 2(2x - 2) ⇒ y = 2x - 2 .........(2) Table of values of equation (1), x | y -- | -- 2 | 2 3 | 0 4 | -2 Table of values of equation (2), x | y -- | -- 0 | -2 1 | 0 2 | 2 Steps of construction : 1. Plot the points (2, 2), (3, 0) and (4, -2) and join them to form equation (1). 2. Plot the points (0, -2), (1, 0) and (2, 2) and join them to form equation (2). 3. The lines intersect at A(2, 2), which is the required solution. Hence, above pair of equations has a unique solution i.e. x = 2 and y = 2.

Mathematics

Which of the following pairs of linear equations are consistent/inconsistent ? If consistent, obtain the solution graphically :
2x + y - 6 = 0, 4x - 2y - 4 = 0

Linear Equations

Related Questions

Which of the following pairs of linear equations are consistent/inconsistent ? If consistent, obtain the solution graphically :
x + y = 5, 2x + 2y = 10

Which of the following pairs of linear equations are consistent/inconsistent ? If consistent, obtain the solution graphically :
x - y = 8, 3x - 3y = 16

Which of the following pairs of linear equations are consistent/inconsistent ? If consistent, obtain the solution graphically :
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Mathematics

Which of the following pairs of linear equations are consistent/inconsistent ? If consistent, obtain the solution graphically :2x + y - 6 = 0, 4x - 2y - 4 = 0

Linear Equations

Related Questions

Which of the following pairs of linear equations are consistent/inconsistent ? If consistent, obtain the solution graphically :x + y = 5, 2x + 2y = 10

Which of the following pairs of linear equations are consistent/inconsistent ? If consistent, obtain the solution graphically :x - y = 8, 3x - 3y = 16

Which of the following pairs of linear equations are consistent/inconsistent ? If consistent, obtain the solution graphically :2x - 2y - 2 = 0, 4x - 4y - 5 = 0

Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is 36 m. Find the dimensions of the garden.

Which of the following pairs of linear equations are consistent/inconsistent ? If consistent, obtain the solution graphically :
2x + y - 6 = 0, 4x - 2y - 4 = 0

Which of the following pairs of linear equations are consistent/inconsistent ? If consistent, obtain the solution graphically :
x + y = 5, 2x + 2y = 10

Which of the following pairs of linear equations are consistent/inconsistent ? If consistent, obtain the solution graphically :
x - y = 8, 3x - 3y = 16

Which of the following pairs of linear equations are consistent/inconsistent ? If consistent, obtain the solution graphically :
2x - 2y - 2 = 0, 4x - 4y - 5 = 0