Is the following pair of linear equations consistent? Justify your answer, (-3)x-4y=12 and 3x+4y=13

Question

Answer

-3x-4y=12---(1),
3x+4y=13--(2),
a1/a2=-3/3=-1,
b1/b2=-4/4=-1,
c1/c2=12/13,
from the above---
a1/a2=b1/b2 is not equal to c1/c2,
so, the pair of linear equations have no solution and are inconsistent

Answer

Consistent means having any solution..

Here a1=-3, b1=-4, c1=-12
and a2=3, b2=4, c1=-13

So a1/a2 = -1
b1/b2 = -1
c1/c2 = 12/13

Since a1/a2 = b1/b2 not equal to c1/c2.

So this pair of equation will be parallel, thus having no solution....

Hence, it is inconsistent.

I HOPE IT WILL HELP U...!!

Answer

Introduction:
The given pair of linear equations is (-3)x - 4y = 12 and 3x + 4y = 13. In order to determine if the pair is consistent, we need to analyze the equations and see if there is a solution that satisfies both equations simultaneously.

Method:
To determine the consistency of the pair of linear equations, we can use the concept of solving systems of equations. There are three possible outcomes when solving a system of linear equations:
1. The system has a unique solution, meaning there is only one point of intersection between the two lines represented by the equations.
2. The system has infinitely many solutions, meaning the two lines are coincident or overlapping.
3. The system has no solution, meaning the two lines are parallel and do not intersect.

Solving the System:
To find the solution, we can either use the method of substitution or elimination. Let's use the elimination method to solve the given pair of linear equations.

Step 1: Multiply the second equation by -1 to eliminate the y variable.
-(-3x - 4y = 12)
3x + 4y = -13

Step 2: Add the modified second equation to the first equation to eliminate the y variable.
(-3x - 4y = 12) + (3x + 4y = -13)
0 = -1

Analysis of the Solution:
The resulting equation 0 = -1 is not true for any value of x or y. This implies that there is no solution that satisfies both equations simultaneously. Therefore, the given pair of linear equations is inconsistent.

Conclusion:
The pair of linear equations (-3)x - 4y = 12 and 3x + 4y = 13 is inconsistent, as there is no solution that satisfies both equations.

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