Classify each system. the system shown below is . x + 3y = 4 3x + 9y = 12 the system shown below is . 3x – 4y = 12 6x – 8y = 21 the system shown below is . 2x – 3y = 8 –3x + 2y = 8

The first one is consitent and dependent

The second one is inconsistent

The third one is consistent and independent

The first system is consistent & dependent; the second system is inconsistent; and the third system is consistent & independent.

Step-by-step explanation:

A consistent system is a system that has at least one solution.  A dependent system is a system that has infinite solutions, because the equations describe the same line.  An independent system is a system that has one solution.  

An inconsistent system is a system that has no solution because the lines are parallel.

The first system is

To solve this, we would make the coefficients of y the same.  We would do this by multiplying the top equation by 3:

We have the same equation; thus this system is consistent and dependent.

The second system is

To solve this, we will make the coefficients of x the same; we will do this by multiplying the top equation by 2:

We have two equations that have the same slope but different y-intercepts; these lines are parallel and thus are inconsistent.

The third system is

To solve this, we will make the coefficients of x the same; we will do this by multiplying the top equation by 3 and the bottom equation by 2:

Now we will add the two equations:

Divide both sides by -5:

-5y/-5 = 40/-5

y = -8

Now substitute this into the first equation:

2x-3(-8) = 8

2x+24 = 8

Subtract 24 from each side:

2x+24 - 24 = 8-24

2x = -16

Divide both sides by 2:

2x/2 = -16/2

x = -8

The solution is (-8, -8); thus the system is consistent and independent.

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.

a 270° rotation about point p says on e d g e n u it y (had to space it out because it says it's a misspelling so i couldn't submit it