solve the following pairs of Linear equations by the method of substitute
2x + 3y =5,2x+3y=7​

2 thoughts on “solve the following pairs of Linear equations by the method of substitute <br />2x + 3y =5,2x+3y=7​”

1. x= 3 and y= 1 is the solution of this question

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2. Step-by-step explanation:

   Given :–

   2x + 3y =5

   2x+3y=7

   To find:–

   Solve the following pairs of Linear equations by the method of substitution ?

   Solution:–

   Given pair of linear equations in two variables are

   2x + 3y = 5

   =>2x + 3y -5 = 0

   a1 = 2

   b1 = 3

   c1 = -5

   and

   2x+3y=7

   => 2x + 3y -7 = 0

   a2 = 2

   b2 = 3

   c2 = -7

   now

   a1/a2 = 2/2=1

   b1/b2 = 3/3=1

   c1/c2 = -5/-7 = 5/7

   We have

   a1/a2 = b1/b2 ≠c1/c2

   So given pair of linear equations in two variables are inconsistent or parallel lines with no solution.

   Answer:–

   No Solution for the given pair of linear equations in two variables.

   Check:–

   2x + 3y = 5

   => 2x = 5-3y

   => x = (5-3y)/2

   On substituting this value in 2x+3y = 7 then

   => 2(5-3y)/2+3y = 7

   => 5-3y+3y=7

   => 5=7

   But this is not true since 5≠7

   So they have no solution.

   Used formulae:–

   • Substitution method
   • a1x+b1y+c1=0 and a2x+b2y+c2=0 are the pair of linear equations in two variables
   • if a1/a2≠b1/b2≠c1/c2 they are consistent and independent lines or intersecting lines with a unique solution.
   • If a1/a2=b1/b2≠c1/c2 then they are Inconsistent or Parallel lines with no solution.
   • If a1/a2=b1/b2=c1/c2 then they are consistent and dependent lines or coincident lines with infinitely number of many solutions.

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