1. what is the solution of the system?
− + 2 = 4
−4 + = −5

2. how many solutions does the system have?
−2 + = 3
4 − 4 =

3. how many solutions does the system have?
3 + = 5
−2 = 6 − 10

4. how many solutions does the system have?
− − 2 = −14
4 = −2 − 12

6. solve the following system using substitution or elimination.
3 + 3 = 27
− 3 = −11

7. solve the following system using substitution or elimination.
2 + 3 = 9
+ 5 = 8

and if you don't mind could you explain how you got your answers

The given system of equations has solutions below:

1) The solution is (2,3)

2) The solution is ()

3) The solution is infinitely many solutions

4) No solution

Step-by-step explanation:

Given system of equation are

To solve equation by using elimination method

Multiply eqn (2) into 2

Now subtracting (1) and (3)

_________________

7x=14

x=

Substitute x=2 in equation (1)

-2+2y=4

2y=4+2

y=3

Therefore the solution is (2,3)

2) Given equation is

4y-4=x

Rewritting as below

To solve equation by using elimination method

multiply (2) into 2

Adding (1) and (3)

-2x+y=3

2x-8y=-8

________

-7y=-5

substitute in (1)

Therefore the solution is ()

3) Given equation is

equation (1) can be written as

2(3x+y)=10

3x+y=5

Therefore equations (1) and (2) are same therefore it has infinitely many solutions

4) Given equation is

multiply equation (1) into 2

To solve equation by using elimination method

subtracting (2) and (3)

-2x-4y=28

-2x-4y=12

_______

therefore it has no solution

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

step-by-step explanation: