Question

5. Solve for x and y, x + y = 3 and 7x + y = 2.
1

Answer 1

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

Pair of linear equations

• x + y = 3

and

• 7x + y = 2.

$\large\underline{\sf{To\:Find - }}$

• Value of x and y.

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

Basic 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

Pair of linear equations,

x + y = 3 -----(1)

and

7x + y = 2 ------(2)

From equation (1) we have

$\rm :\longmapsto\:y = 3 - x - - - (3)$

On substituting equation (3) in equation (2), we get

$\rm :\longmapsto\:7x + 3 - x = 2$

$\rm :\longmapsto\:6x + 3 = 2$

$\rm :\longmapsto\:6x = - 1$

$\rm :\implies\: \boxed{ \bf{x \: = \: - \: \dfrac{1}{6} }} - - - (4)$

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

$\rm :\longmapsto\:y = 3 - \bigg( - \dfrac{1}{6} \bigg)$

$\rm :\longmapsto\:y = 3 + \dfrac{1}{6}$

$\rm :\longmapsto\:y = \dfrac{18 + 1}{6}$

$\rm :\implies\: \boxed{ \bf{y \: = \: \dfrac{19}{6} }}$

$\bf\implies \boxed{ \bf{ \:x = - \dfrac{1}{6} }} \: \: \sf \: \: \: and \: \: \: \: \boxed{\bf\: y \: = \dfrac{19}{6} }$

Additional Information :-

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.

• Step 3: Solve this new equation for variable.

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