On comparing the ratios a1/b1, b2/c2, c1/c2, find out whether the following pairs of linear equations are consistent or inconsistent: 3x + 2y = 5 and 2x - 3y = 7

By Ritesh|Updated : November 14th, 2022

On comparing the ratios a1/b1, b2/c2, c1/c2, the pairs of linear equations 3x + 2y = 5, 2x - 3y = 7 are consistent. Steps to find out whether the following pairs of linear equations are consistent or inconsistent:

Step 1: examining the circumstance under which parallel or concurrent lines intersect

If a pair of linear equations are provided to us,

a1x + b1y + c1 = 0

a2x + b2y + c2 = 0

lines are consistent, if a1/a2 ≠ b1/b2 and a1/a2 = b1/b2 = c1/c2

lines are inconsistent if a1/a2 = b1/b2 ≠ c1/c2

Step 2: Verify the equations in the provided set:

The equations are:

3x + 2y = 5

2x - 3y = 7

Now by comparing the given equations with the standard form:

a1x + b1y + c1 = 0

a2x + b2y + c2 = 0

a1 = 3, a2 = 2, b1= 2, b2 = -3, c1 = 5, c2 = 7

a1/a2 = 3/2

b1/b2 = 2/-3

c1/c2 = 5/7

Since a1/a2 ≠ b1/b2, As a result, there is only one way to solve the given equations because they cross at one point.

As a result, the given set of linear equations is valid.

Summary:

On comparing the ratios a1/b1, b2/c2, c1/c2, find out whether the following pairs of linear equations are consistent or inconsistent: 3x + 2y = 5 and 2x - 3y = 7

On comparing the ratios a1/b1, b2/c2, c1/c2, the pairs of linear equations 3x + 2y = 5, 2x - 3y = 7 are consistent. An equation is a mathematical assertion in which the algebraic expression is separated by an equal sign (=). Equations of degree 1 are linear equations.

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