Question

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

Answer 1

Answer:

I hope it will be help full for you

Answer 2

Basic Concept :-

There are 4 methods to solve this type of pair of linear equations.

• 1. Method of Substitution

• 2. Method of Eliminations

• 3. Method of Cross Multiplication

• 4. Graphical Method

We prefer here Method of Eliminations.

To solve systems using elimination, follow this procedure:

The Elimination Method

• Step 1: Multiply each equation by a suitable number so that the two equations have the same leading coefficient.

• Step 2: Subtract the second equation from the first to reduce the equation to one variable.

• Step 3: Solve this new equation for one variable.

• Step 4: Substitute the value of this variable into either of Equation 1 or Equation 2 above and solve for other variable.

Let's solve the problem now!!

Given equations are

$\rm :\longmapsto\:ax + by = a - b - - (1)$

$\rm :\longmapsto\:bx - ay = a + b - - (2)$

On multiply equation (1) by b, we get

$\rm :\longmapsto\:abx + {b}^{2} y = ab - {b}^{2} - - (3)$

On multiplying equation (2) by a, we get

$\rm :\longmapsto\:abx - {a}^{2} y = {a}^{2} + ab - - (4)$

Subtracting equation (4) from equation (3), we get

$\rm :\longmapsto\: {b}^{2} y + {a}^{2} y = - {b}^{2} - {a}^{2}$

$\rm :\longmapsto\:y \: \cancel{( {a}^{2} + {b}^{2})} = - \: \cancel{( {b}^{2} + {a}^{2})}$

$\bf\implies \:y \: = \: - \: 1$

Now, Substitute the value of y in equation (1), we get

$\rm :\longmapsto\:ax - b = a - b$

$\rm :\longmapsto\:ax = a$

$\bf\implies \:x \: = \: 1$

$\overbrace{ \underline { \boxed { \bf \therefore \: The \:solution\: is \: x \: = 1 \: \: and \: \: y \: = \: - 1)}}}$