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Pair of Linear Equations in Two Variables

Short Answer Type

151.

Solve the following pair of linear equations:

px + qy = p - q
qx - py = p + q

163 Views

Long Answer Type

152.

Solve the following pair of linear equations:

ax + by = c
bx + ay = 1 + c

195 Views

153. $straight x over straight a minus straight y over straight b equals 0 ax plus by equals straight a squared plus straight b squared$

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The given pair of linear equations is

straight x over straight a minus straight y over straight b equals 0 space space space space space space space space space space space space space space space space space space space space... left parenthesis straight i right parenthesis ax plus bt equals straight a squared plus straight b squared space space space space space space space space space space space space space space space... left parenthesis ii right parenthesis

From equation (i), we have

straight y over straight b equals straight x over straight a rightwards double arrow space space space straight y equals straight b over straight a straight x space space space space space space space space space space space space space space space space space space.... left parenthesis iii right parenthesis

Substituting the value of y in equation (ii), we get

ax plus straight b open parentheses straight b over straight a straight x close parentheses equals straight a squared plus straight b squared rightwards double arrow space space ax plus straight b squared over straight a straight x equals straight a squared plus straight b squared rightwards double arrow space straight a squared straight x plus straight b squared straight x equals straight a left parenthesis straight a squared plus straight b squared right parenthesis rightwards double arrow space space straight x equals fraction numerator straight a open parentheses straight a squared plus straight b squared close parentheses over denominator straight a squared plus straight b squared end fraction equals straight a

Substituting the value of x in (iii), we get

straight y equals straight b over straight a straight x rightwards double arrow space space straight y equals straight b over straight a cross times straight a equals straight b

Hence, X= a, y = b

150 Views

Short Answer Type

154.

Solve the following pair of linear equations:

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143 Views

155.

Solve the following pair of linear equations:

152x – 378y = – 74
–378x + 152y = – 604

931 Views

Long Answer Type

156.

ABCD is a cyclic quadrilateral (see Fig. 3.7). Find the angles of the cyclic quadrilateral.

781 Views

Short Answer Type

157.

Find the number of solutions of the follow ing pair of linear equations :
x + 2y - 8 = 0
2x + 4y = 16

146 Views

158.

Is the pair of linear equations consistent:
2x - 3y + 2 = 0,3x - 5y + 4 = 0.

82 Views

159. Find the value of k so that the followings systemk of a equations has no solution.
3x - y - 5 = 0; 6x - 2y - k = 0

589 Views

160. For what value of m, the pair of linear equations mx = 2y, 2x - y + 5 = 0 has unique solution.

368 Views