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Pair of Linear Equations in Two Variables

Short Answer Type

161. For what value of k, the pair of linear equations 3x - ky + 7 = 0,x - 2y + 5 = 0 has unique solution.

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162. Given below are three equations. Two of them have infinite solutions and two of them have no solution. State the two pairs :

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163. Show that x = 1 and y = 1 is a solution of the pair of equations 2x + 3y = 5. 5x - 2y = 3.

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164.

Write whether the following pair of linear equations is consistent or not.

x + y = 14
x - y = 4

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165.
Find the value of k so that the following system of equations has infinite solutions:

3x - y - 5 = 0; 6x - 2y + k = 0

Here, a₁ = 3, b₁ = -1 and c₁ = -5
a₂ = 6, b₂ = -2 and c₂ = k

$therefore space straight a subscript 1 over straight a subscript 1 equals 3 over 6 equals 1 half comma space space space straight b subscript 1 over straight b subscript 2 equals fraction numerator negative 1 over denominator negative 2 end fraction equals 1 half comma space straight c subscript 1 over straight c subscript 2 equals fraction numerator negative 5 over denominator straight k end fraction Now comma space space space space space space space space space space space space space space space space space fraction numerator negative 5 over denominator straight k end fraction equals 1 half rightwards double arrow space space space space straight k space space equals space minus 10$
Hence the given system will have infinite no. of solution if k = -10.

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166. Find the value of k for which the pair of equations kx - 4y = 3; 6x - 12y = 9 has an infinite number of solution.

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167. Check whether x = 3, y = -1 and x = -6, y = 5 are solutions of the system of linear equations 2x + 3y = 3 and 6x + 9y - 9 = 0. Does the given system has an infinite number of solutions ? Give reason.

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168. Obtain the condition for the following system of linear equations to have a unique solution ax + by = c and lx + my = n.

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169.

Given the linear equation 2a + 3y - 8 = 0, write another linear equation in two variables such that the geometrical representation of the pair so formed is :

(i) parallel lines

(ii) intersecting lines

(iii) coincident lines.

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