Find whether the following pair of linear equations is consistent or inconsistent:3x + 2y = 86x – 4y = 9

To determine whether the given pair of linear equations is consistent or inconsistent, we can use the method of elimination or substitution.

Let's use the method of elimination to solve the equations:

Step 1: Multiply the first equation by 3 and the second equation by 2 to make the coefficients of x in both equations equal:

3(3x + 2y) = 3(86) 2(6x – 4y) = 2(9)

Simplifying these equations, we get:

9x + 6y = 258 12x – 8y = 18

Step 2: Add the two equations together to eliminate the y variable:

(9x + 6y) + (12x – 8y) = 258 + 18 21x – 2y = 276

Step 3: Divide the equation by 2 to simplify it further:

(21x – 2y)/2 = 276/2 10.5x – y = 138

Now, we have a new equation: 10.5x – y = 138

Step 4: Compare this equation with the original equations:

10.5x – y = 138 6x – 4y = 9

We can see that the coefficients of x and y are different in the two equations. Therefore, the given pair of linear equations is inconsistent.

In conclusion, the pair of linear equations 3x + 2y = 86 and 6x – 4y = 9 is inconsistent.