Describe how to interpret the solution of the system of
equations to solve a problem.

Graphing is a very useful tool to solve a system of equations but the only major disadvantage is that it is very time-consuming. So, we can solve the system of equations quickly by isolation one variable in one equation and then we get the answer by substituting the resulting expression for the variable in the other equation.

Step-by-step explanation :

Step 1:

Consider the system of equations:

5x + y =13  

3x=15 - 3y

Step 2 :  

y is the easiest variable to isolate in the first equation, because it has no coefficient:

y = 13 - 5x

Step 3 :

In the second equation, substituting for y :

3x = 15 - 3(13 - 5x)

Step 4 :

Solve the equation:

3x = 15 - 39 + 15x

3x = 15x - 24

-12x = - 24

x = 2

substituting this x-value into the "isolated equation" to find y:

y = 13 - 5x = 13 - 5(2) = 13 - 10 = 3

The solution to the system is (2, 3).  This point is used to check for solutions in both equations.

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.

(2,20) means that the 2 is 2 hours and 20 is 20$. so there both 20$ for 2 hours only the same price. like it says. so, the dunk tank and the bounce house are the same price (20$) for the same amount of time (2 hours).

hope i