6. how many solutions does this system of linear
equations have? explain.
3y + 6x = 12
8x + 4y = 16
: )

Infinitely many solutions

Step-by-step explanation:

Let's take the first equation.

3y + 6x = 12

Now take common,

3( y + 2x ) = 12

So, y + 2x = 4

Lets take 2nd equation

4y + 8x = 16

Take common,

4(y + 2x) = 16

So, y + 2x = 4.

Two lines with same equation have infinitely many solutions. These two equations are the same so there are infinitely many solutions.

look at the picture.

1.

ef : ab = 2 : 3

gf : cb = 2 : 3

gh : cd = 2 : 3

he : da = 2 : 3

2.

∠a ≅ ∠e

∠b ≅ ∠f

∠c ≅ ∠g

∠d ≅ ∠h

3.

use pythagorean theorem:

the length of the abcd trapezoid sides:

|ab| = 3 cm

|bc| = 10 cm

|cd| = 3(3) cm = 9 cm

|da| = 8 cm

the perimeter of abcd = 3 + 10 + 9 + 8 = 30 cm

the ratio of perimeters of the tarapezoids is equal 2 : 3.

substitute:

      cross multiply

      divide both sides by 3