Without graphing, is the system independent, dependent, or inconsistent?

2 answers:

7 0

Putting the equations into standard form helps me identify dependent and inconsistent systems. In standard form, the leading coefficient is positive, and all numbers are mutually prime (have no common factors).

1.) 2x + y = -9 . . . . . . multiply the original equation by -1

... 3x - 4y = -8 . . . . . . the system is independent

These two equations will give rise to a single solution.

_____

2.) 4x + y = 4 . . . . . . divide the original equation by 3

... 4x + y = 5 . . . . . . . the system is inconsistent

These two equations describe parallel lines, so will not have a point of intersection. There are no values of x and y that can satisfy both equations.

eimsori [14]4 years ago

5 0

1. independent

2. inconsistent

You might be interested in

Please help me out

Tema [17]

Answer:

UwU thank you

please remember to smile, because when you do the whole world gets brighter

-Todo <3

Step-by-step explanation:

7 0

3 years ago

If you are solving the equation 1/(x-4)+1=14/(x+2) by factoring, which of the following equations would you use the zero product

Grace [21]

Answer:

The equation that would be used for the zero product property on will be (x-5)(x-10)=0

Option B is correct.

Step-by-step explanation:

We need to solve the equation $\frac{1}{(x-4)}+1=\frac{14}{x+2}$

Solving the equation:

$\frac{1}{(x-4)}+1=\frac{14}{x+2}\\\frac{1+(x-4)}{x-4}= \frac{14}{x+2}\\\frac{1+x-4}{x-4}= \frac{14}{x+2}\\\frac{x-3}{x-4}= \frac{14}{x+2}\\Cross\: Multiply\\(x-3)(x+2)=14(x-4)\\x(x+2)-3(x+2)=14x-56\\x^2+2x-3x-6=14x-56\\x^2-x-6-14x+56=0\\x^2-x-14x-6+50=0\\x^2-15x+50=0$