Solve the following system of equations: x − 2y = 14 x + 3y = 9 a. (1, 12) b. (−1, −12) c. (12, −1) d. (12, 1)

Answer

The correct answer is C. (12, -1).

Step-by-step

I will solve the system of equation using the substitution method. I will solve for x in the second equation and then substitute that value in for x in the first equation.

x - 2y = 14

x + 3y = 9

Part 1: Solve for x in the second equation

x + 3y = 9

x + 3y - 3y = 9 - 3y

x = 9 - 3y

x = -3y + 9

Part 2: Substitute -3y + 9 in for x in the first equation and solve for y

x - 2y = 14

(-3y + 9) - 2y = 14

-5y + 9 = 14

-5y + 9 - 9 = 14 - 9

-5y = 5

-5y / -5 = 5 / -5

y = -1

Part 3: Use the value for y to solve for x in the second equation

x = -3y + 9

x = -3(-1) + 9

x = 3 + 9

x = 12

Part 4: Write your answer as a coordinate with x and y values

x = 12; y = -1

(12, -1)

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

idk

step-by-step explanation: