Question

4x+2y=-6
-2x-y=8
a.consistent and independent
b.inconsistent
c.consistent and dependent
d.none of the above

Answer 1

To determine the nature of the system of equations given:

1. The first equation: \( 4x + 2y = -6 \)
2. The second equation: \( -2x - y = 8 \)

Let's solve this system.

First, we can manipulate the equations to see if they have a unique solution, no solution, or infinitely many solutions.

**Step 1: Solve the first equation for \( y \)**

From \( 4x + 2y = -6 \):

\[
2y = -6 - 4x
\]
\[
y = -3 - 2x
\]

**Step 2: Substitute \( y \) into the second equation**

Substituting \( y = -3 - 2x \) into \( -2x - y = 8 \):

\[
-2x - (-3 - 2x) = 8
\]
\[
-2x + 3 + 2x = 8
\]
\[
3 = 8
\]

This is a contradiction. Since both of the simplified equations lead to an impossible statement (3 does not equal 8), the system has no solutions.

**Conclusion:**
Since the system of equations has no solution, it is classified as **inconsistent**. Therefore, the answer is:

b. inconsistent