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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

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.

We know that the opposite angles of a cyclic quadrilateral are supplementary, therefore,
∠A + ∠C = 180°
⇒ 4y + 20 + 4x = 480°
⇒ 4x + 4y = 60°
⇒    x + y = 40°    ...(i)
[Dividing throughout by 4]
and ∠B + ∠D = 180°
⇒3y - 5 + 7x + 5= 180°
⇒ 7x + 3y = 180°    ...(ii)
From equation (i), we have
y = 40 - x    ...(iii)
Substituting this value of y in equation (ii), we get
7x + 3(40 - x) = 180°
⇒7x + 120 - 3x = 180°
⇒    4x = 60
$rightwards double arrow space space space straight x space equals 60 over 4 equals 15 degree$

Substituting x = 15 in equation (iii), we get
y = 40 - x
= 40 - 15 = 25°
Hence, required angles be
∠A = 4y + 20 = 4 × 25 + 20 = 120
∠B = 3y - 5 = 3 × 25 - 5 = 75 - 5 = 70
∠C = 4x = 4 × 15 = 60°
∠D = 7x + 5 = 7 × 15 + 5
= 105 + 5 = 110°

781 Views