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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 BYJU'S Exam Prep
Updated on: September 25th, 2023
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.
