2y = x + 3
5y = x - 7
7
what is the solution set of the given system?
{f-13.-4/3}}
{(1/3,4/3)
{l-29/3.-10/3}}
{(29/3, 10/3)

Solution:  { -29/3 , -10/3 }

Step-by-step explanation:

2y = x + 3  > equ 1

5y = x - 7    equ 2

equ 1 - equ s  >     -3y = 10

                                         y =  -10/3

Put y = -10/3 in equ 1

        2 * (-10/3)   = x + 3

         -20/3         = x + 3

          (-20/3) - 3   = x

        (-20/3) - (9/3)  = x

         (-20 - 9) / 3    =x

                x = -29/3

Solution:  { -29/3 , -10/3 }

For this case we must solve the following system of equations:

We clear "x" from the second equation:

We substitute in the first equation:

We look for the value of the variable "x":

Thus, the solution of the system is given by:

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.