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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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The given system of equations may be written as

Putting the value of x in (ii), we get
(a + b)x + (a + b) y = a² + b²⇒(a + b) (a + b) + (a + b)y = a² + b²⇒ (a + b)² (a + b)y = a² + b²⇒(a + b)y = (a² + b²) - (a + b)²⇒ (a + b)y = (a² + b²) - (a² + b² + 2ab)
⇒ (a + b)y = a² + b² - a² - b² - 2ab
⇒ (a + b)y = - 2ab
$rightwards double arrow space space space straight y equals fraction numerator negative 2 ab over denominator straight a plus straight b end fraction$
Hence,

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