Solve 3x − 2y = −21 and 2x + 5y = 5 using elimination

x = -5 and y = 3

Step-by-step explanation:

There are two equations :

3x − 2y = −21 (1)

2x + 5y = 5 (2)

Multiply equation (1) by 2 and equation (2) by 3.

6x - 4y = -42 ...(3)

6x + 15y = 15 (4)

Subtract equation (4) from (3) :

6x - 4y - (6x + 15y) = -42 -15

-4y -15y = -57

-19y = -57

y = 3

Put y = 3 in equation (2) :

2x + 5(3) = 5

2x = 5-15

2x = -10

x = -5

So, the value of x is (-5) and y = 3.

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

12m

step-by-step explanation:

square root means have of a number so have of 3 is 1.5 then multiply it by 8 and you get your answer!