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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

152x - 378y = -74
-378x + 152y = -604
The given pair of linear equations is
152x - 378y = -74    ...(i)
-378x + 152y = -604    ...(ii)
Adding equation (i) and equation (ii), we get
-226x - 226y = -678
⇒    x + y = 3    ...(iii)
[Dividing throughout by -226]
Subtracting equation (ii) from equation (i), we get
530x - 530y = 530
⇒    x - y = 1    ...(iv)
[Dividing throughout by 530]
Adding equation (iii) and equation (iv), we get
2x = 4

$rightwards double arrow space space space space straight x space 4 over 2 equals 2$
Subtracting equation (iv) from equation (iii), we get
2y = 2
$rightwards double arrow space space space y equals 2 over 2 equals 1$
Hence, the solution of the given pair of linear equations is x = 2, y = 1.