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

Without graphing, the system -2x - y = 9 and 3x - 4y = -8 is independent and consistent.

Solution:

Given, system of equations are -2x – y = 9 and 3x – 4y = -8

We have to find the type of equations i.e. independent or dependent or inconsistent.

Now, for that we have to solve the given system of equations to derive an conclusion.

So, now, -2x – y = 9 ⇒ 2x + y = -9 ⇒ (1) and 3x – 4y = -8 → (2)

Here we have to multiply (1) with 4 in order to cancel one of terms.

Then, solving (1) and (2)

11x + 0 = -44

x = -4

Substitute x value in (1)

2(-4) + y = -9

-8 + y = -9

y = 8 – 9

y = -1

So, the system of equations is consistent and it is independent as two equations represents different equation.

Hence, system of equations are independent and consistent.