Question

Without graphing, is the system independent, dependent, or inconsistent? How do you know?

-2 - y = 9
3x - 4y = -8

Answer 1

The answers that you are looking for my friend ;)

1. D

2.A

3.B

4.C (independent)

5. B

Answer 2

Independent

Explanation:

We need to find whether the system of equations
`-2-y=9` and
`3x-4y=-8` are independent, dependent, or inconsistent.

Now, we know that the general form of a linear equation in two variables is
`ax+by+c=0`

So, the general form of the given equations is
`-y-11=0` and
`3x-4y+8=0`

Now, for a system of equations
`a_(1)x+b_(1)y+c_(1)=0` and
`a_(2)x+b_(2)y+c_(2)=0` , we need to find
`(a_(1))/(a_(2))`,
`(b_(1))/(b_(2))`, and
`(c_(1))/(c_(2))`

Now,
`(a_(1))/(a_(2))=(0)/(3)`

`(b_(1))/(b_(2))=(-1)/(-4)=(1)/(4)`

So, we have
`(a_(1))/(a_(2))\\eq (b_(1))/(b_(2))`

Hence, the system of equations are independent.