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Solve the system of equations

{3x−y=6
{6x+y=21

The easiest way to solve this is by elimination.  

3x - y = 6  

6x + y = 21

Since you have a negative and positive y with the same coefficients (1), they cancel, and you add the other terms so it would look like:

9x = 27  

Then solving for x leaves you with x = 3  

Then you take the x value of three and plug it into to either of the equations, so  

3(3) - y = 6

9 - y = 6  

subtracting 9  

-y = -3  

then dividing by -1  

y = 3  

so the solution is x = 3 y = 3 or (3,3)  

Step-by-step explanation:

step-by-step explanation: h: (- 3, 6)

m: (1, - 2)

o: (7, 6)

r: (- 9, - 2)

midpoint of hm: (- 1, 2)

midpoint of or: (- 1, 2)

therefore, b is the midpoint of both diagonals bisect each other !

to prove the diagonals are perpendicular, show that the product of the slopes = - 1