Question

Solve : ax+by = a-b bx-ay =a+b by elimination by SUBSTITUTION only.

Answer 1

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

Answer 2

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

Given,

Two equations ax+by = a-b and bx-ay =a+b

To Find,

The value of x and y using the substitution method.

Solution,

The given equation is

ax+by=a-b

ax=a-b-by

Using substitution method.

x=a-b-by/a

Substituing the value of x in other equation.

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 the  value of y

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

x=a-b+b/a

x=a/a

x=1

Hence, the value of x is 1 and y is -1.