Question

Find the solution of the pair of linear equation x-3y = 13 and 2y -x =-5.​

Answer 1

Answer:

x=37 And y=8

I have done the sum by comparing two equations

Answer 2

Given

Pair of linear equations

• x - 3y = 13

• 2y - x = - 5

Concept Used :-

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!!

Given first equation is

$\rm :\longmapsto\:x - 3y = 13$

$\rm :\implies\:x = 3y + 13 - - - (1)$

Now,

Second equation is

$\rm :\longmapsto\:2y - x = - 5$

$\rm :\longmapsto\:2y - (3y + 13) = - 5$

$\rm :\longmapsto\:2y - 3y - 13 = - 5$

$\rm :\longmapsto\: - \: y - 13 = - 5$

$\rm :\longmapsto\: - \: y = - 5 + 13$

$\rm :\longmapsto\: - \: y = 8$

$\rm :\implies\:y = - 8$

Put y = - 8 in equation (1), to get

$\rm :\implies\:x = 3 \times ( - 8) + 13$

$\rm :\implies\:x = - 24 + 13$

$\rm :\implies\:x = - 11$

Hence

$\: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \bf \: x = - 11 \: \: \: and \: \: \: y = - 8}$