# Pair Of Linear Equations In Two Variables

#### Question 7:

Solve the following pair of linear equations.

(i) *px*
+ *qy* = *p* − *q*

*qx *− *py* = *p* + *q*

(ii) *ax*
+ *by* = *c*

*bx* + *ay* = 1 + *c*

(iii)

*ax* + *by* = *a*^{2} + *b*^{2}

(iv) (*a*
− *b*) *x* + (*a* + *b*) *y* =* a*^{2}− 2*ab* − *b*^{2}

(*a* + *b*) (*x* + *y*) = *a*^{2} +
*b*^{2}

(v) 152*x*
− 378*y* = − 74

− 378*x *+ 152*y* = − 604

#### Answer:

(i)*px*
+ *qy* = *p* − *q * … (1)

*qx *− *py* = *p* + *q *… (2)

Multiplying equation (1) by *p* and equation (2) by *q*, we
obtain

*p*^{2}*x* + *pqy* = *p*^{2} −
*pq* … (3)

*q*^{2}*x* − *pqy* = *pq* + *q*^{2} …
(4)

Adding equations (3) and (4), we obtain

*p*^{2}*x* + *q*^{2} *x *= *p*^{2}
+ *q*^{2}

(*p*^{2} + *q*^{2}) *x* = *p*^{2}
+ *q*^{2}

From equation (1), we obtain

*p* (1) + *qy* = *p* − *q*

*qy *= − *q*

*y* = − 1

(ii)*ax*
+ *by* = *c* … (1)

*bx* + *ay* = 1 + *c* … (2)

Multiplying equation (1) by *a* and equation (2) by *b*, we
obtain

*a*^{2}*x *+ *aby *= *ac* … (3)

*b*^{2}*x* + *aby* = *b* + *bc* …
(4)

Subtracting equation (4) from equation (3),

(*a*^{2} − *b*^{2}) *x *= *ac*
− *bc* − *b*

From equation (1), we obtain

*ax *+ *by* = *c*

(iii)

Or, *bx* − *ay…*

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