Question

1. If 5x + 2y = 7 and x – 3y = -1, find the value x and y​

Answer 1

$\large\underline{\bold{Given \:Question - }}$

• If 5x + 2y = 7 and x – 3y = -1, find the value x and y

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

Basic Concept Used :-

There are 4 methods to solve pair of linear equations.

• 1. Substitution Method

• 2. Elimination Method

• 3. Cross Multiplication Method

• 4. Graphical Method.

We can use any Method to solve the pair of equations.

Prefer here,

Method of substitution :-

• Solve one of the equations for either x or y.

• Substitute the step 1 solution in the other equation.

• Now solve the new equation obtained using elementary arithmetic operations.

• Finally, solve the equation to find the value of the second variable.

Let's now solve the problem!!

Given,

Pair of linear equations,

• x - 3y = - 1 ------(1)

and

• 5x + 2y = 7 -------(2)

Now,

• From equation (1) we have,

$\sf \: x = 3y - 1 - - - (3)$

Now,

• Substitute the (3) in equation (2), we get

$\sf \: 5(3y - 1) + 2y = 7$

$\sf \: 15y - 5 + 2y = 7$

$\sf \: 17y = 12$

$\therefore \: \: \boxed{ \bf{y \: = \: \dfrac{12}{17} }}$

• Substituting the value of y in equation (3), we get

$\sf \: x \: = \: 3 \times \dfrac{12}{17} - 1$

$\sf \: x = \dfrac{36}{17} - 1$

$\sf \: x = \dfrac{36 - 17}{17}$

$\therefore \: \: \boxed{ \bf{x \: = \: \dfrac{19}{17} }}$