This is the basic and conceptual question from linear equations in two variables in which we have given two equations a²x+b²y=c², b²x+a²y=d² and we have been asked to find the value of variables x and y from the given equations

Kindly solve the equations

RS Aggarwal, Class 10, chapter 3B, question no 49

Hope it helps you.

Sol:

The given equations are

a

2

x + b2

y = c2

………(i)

b

2

x + a2

y = d2

………(ii)

Multiplying (i) by a2

and (ii) by b2

and subtracting, we get

a

4

x – b

4

x = a2

c

2

– b

2

d

2

⇒x =

𝑎

2𝑐

2−𝑏

2𝑑

2

𝑎4− 𝑏4

Now, multiplying (i) by b2

and (ii) by a2

and subtracting, we get

b

4

y – a

4

y = b2

c

2

– a

2

d

2

⇒y =

𝑏

2𝑐

2−𝑎

2𝑑

2

𝑏4− 𝑎4

Hence, x = 𝑎

2𝑐

2−𝑏

2𝑑

2

𝑎4− 𝑏4

and y = 𝑏

2𝑐

2−𝑎

2𝑑

2

𝑏4− 𝑎4

.

Solve for x and y:

a

2

x + b2

y = c2

, b2

x + a2

y = d2

Sol:

The given equations are

a

2

x + b2

y = c2

………(i)

b

2

x + a2

y = d2

………(ii)

Multiplying (i) by a2

and (ii) by b2

and subtracting, we get

a

4

x – b

4

x = a2

c

2

– b

2

d

2

⇒x =

𝑎

2𝑐

2−𝑏

2𝑑

2

𝑎4− 𝑏4

Now, multiplying (i) by b2

and (ii) by a2

and subtracting, we get

b

4

y – a

4

y = b2

c

2

– a

2

d

2

⇒y =

𝑏

2𝑐

2−𝑎

2𝑑

2

𝑏4− 𝑎4

Hence, x = 𝑎

2𝑐

2−𝑏

2𝑑

2

𝑎4− 𝑏4

and y = 𝑏

2𝑐

2−𝑎

2𝑑

2

𝑏4− 𝑎4

.