Question

Q: 10 Solve: ax + by = a - b and bx - ay = a + b​

Answer 1

Answer:

x=1

y=-1

Step-by-step explanation:

ax+by=a-b

ax=a-b-by

x=a-b-by/a←

bx-ay=a+b

substituting

b(a-b-by/a)-ay=a+b

ab-b²-b²y/a-ay=a+b

ab-b²-b²y-a²y/a=a+b

ab-b²-(b²+a²)y=a²+ab

-(b²+a²)y=a²+ab-ab+b²

(b²+a²)y=-(a²+b²)

y=-(a²+b²)/a²+b²

y=-1←

substituting value of y

x=a-b-b(-1)/a

x=a-b+b/a

x=a/a

x=1

Hope it helps!

Answer 2

Answer:-

The value of x is 1 and the value of y is -1 respectively.

Explanation:-

ax + by = a - b ........(i)

bx - ay = a + b ........(ii)

Solving the following pair of linear simultaneous equations by elimination method.

Multiplying eqn.(i) by b, we get:-

abx + b²y = ab - b² ......(ii)

Multiplying eqn.(ii) by a, we get:-

abx - a²y = a² + ab ........(iii)

Subtracting eqn. (i) & (ii)

abx + b²y = ab - b²

abx - a²y = ab + a²

- + - -

________________________

b²y + a²y = - a² - b²

or, y(b²+a²) = - (a²+b²)

or, y = -(a² +b²)/(a²+b²)

or, y = - 1

Hence, the value of y is -1

Putting the value of y in eqn.(i), we get:-

ax + by = a - b

=> ax + b.(-1) = a - b

=> ax - b = a - b

=> ax = a - b + b

=> ax = a

=> x = a/a

=> x = 1

Hence, the value of x is 1.