Using elimination method, simultaneously solve this equation: 2y+3x=7 and 4x+3y=15

x = -9   , y = 14

Step-by-step explanation:

3x + 2y = 7 equation 1

4x + 3y = 15   equation 2

Solving using elimination method , we have to decide the variable we are eliminating first , we could eliminate x or y. If we are to eliminate y first , we will multiply equation 1 by 3 and equation 2 by 2 so that the coefficient of y can be the same. The equation then becomes

3( 3x + 2y = 7 )

2 ( 4x + 3y = 15 )

Expanding , we have

9x + 6y = 21 equation 3

8x + 6y = 30 equation 4

Now that the coefficient of y is the same , we will subtract equation 4 from equation 3 to eliminate y , we have

x = -9

Substitute y = -9 into equation 1 to find the value of x , we have :

3( -9 ) + 2y = 7

-27 + 2y = 7

2y = 7 + 27

2y =34

y = 34/2

y = 14

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet