Question

solve the followning linear equation : x-2y=-20,3x-5y=-24​

Answer 1

$\large\underline{\sf{Given- }}$

Pair of linear equations are

$\: \: \: \: \: \: \: \: \: \bull \: \sf \: x - 2y = - \: 20 - - - (1)$

$\: \: \: \: \: \: \: \: \bull \: \sf \: 3x - 5y = - \: 24 - - - (2)$

$\large\underline{\sf{Solution-}}$

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 Substitution

To solve systems using substitution, follow this procedure:

• Select one equation and solve it to get one variable in terms of second variables.

• In the second equation, substitute the value of variable evaluated in Step 1 to reduce the equation to one variable.

• Solve the new equation to get the value of one variable.

• Substitute the value found in to any one of two equations involving both variables and solve for the other variable.

Let's solve the problem now!!

Calculation :-

Given pair of equations is

$\: \: \: \: \: \bull \: \sf \: x - 2y = - \: 20 - - - (1)$

and

$\: \: \: \: \: \bull \: \sf \: 3x - 5y = - \: 24 - - - (2)$

From equation (1),

$\rm :\longmapsto\:x - 2y = - 20$

$\bf\implies \:x = 2y - 20 - - - (3)$

On substituting the value of 'x' in equation (2), we get

$\rm :\longmapsto\:3(2y - 20) - 5y = - 24$

$\rm :\longmapsto\:6y - 60 - 5y = 24$

$\bf\implies \:y \: = \: 84 - - - (4)$

On substituting the value of 'y' in equation (3), we get

$\rm :\longmapsto\:x = 2 \times 84 - 20$

$\rm :\longmapsto\:x = 168 - 20$

$\bf\implies \:x \: = \: 148$