Without graphing is the system independent dependent or inconsistent -2x - y = 9 and 3x - 4y = -8

Solution:

The above two equations are linear equations which can be solved simultaneously.

Therefore rewriting the equations we get:

-2x - y = 9 --- (1)

3x - 4y = -8 --- (2)

Multiplying (1) by 3 and (2) by 2 and then adding the two we get:

-6x - 3y = 27
6x - 8y = -16
------------------
0 - 11y = 11

Therefore,

y = 11/(-11)

= -1

Substituting the value of y = -1 in equation (1), we get

⇒ -2x - (-1) = 9

⇒ -2x + 1 = 9

⇒ -2x = 9 - 1

⇒ -2x = 8

⇒ x = 8/(-2)

⇒ x = -4

Since the linear equations can be solved simultaneously and have a unique solution then the two equations are independent.

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Without graphing is the system independent dependent or inconsistent -2x - y = 9 and 3x - 4y = -8

Summary:

Without graphing is the system it has been established that the system of equations -2x - y = 9 and 3x - 4y = -8 are independent as they have a unique solution.