Question

PLEASE HELP!!! 100 POINTS!!! EASY!!

Which ordered pair is the solution to the system of equations?

{y=3x−12
4x+6y=−6


(6, −5)

(0, −12)

(3, −3)

(4, −7)

Answer 1

Answer:

(3, -3)

Step-by-step explanation:

METHOD 1.

Put the coordinates of the given points to the equations and check the equality.

$\left\{\begin{array}{ccc}y=3x-12&(1)\\4x+6y=-6&(2)\end{array}\right$

for (6, -5)

(1)

-5 = 3(6) - 12

-5 = 18 - 12

-5 = 6   FALSE

for (0, -12)

(1)

-12 = 3(0) - 12

-12 = 0 - 12

-12 = -12    TRUE

(2)

4(0) + 6(-12) = -6

0 - 72 = -6

-72 = -6    FALSE

for (3, -3)

(1)

-3 = 3(3) - 12

-3 = 9 - 12

-3 = -3    TRUE

(2)

4(3) + 6(-3) = -6

12 - 18 = -6

-6 = -6    TRUE

for (4, -7)

(1)

-7 = 3(4) - 12

-7 = 12 - 12

-7 = 0    FALSE

ANSWER: (3, -3)

METHOD 2:

Solve the system of equations:

$\left\{\begin{array}{ccc}y=3x-12&(1)\\4x+6y=-6&(2)\end{array}\right$

substitute (1) to (2):

$4x+6(3x-12)=-6\qquad|\text{use the distributive property}\\4x+(6)(3x)+(6)(-12)=-6\\4x+18x-72=-6\qquad|\text{add 72 to both sides}\\22x=66\qquad|\text{divide both sides by 22}\\\boxed{x=3}$

put it to (1):

$y=3(3)-12\\y=9-12\\\boxed{y=-3}$

$\left\{\begin{array}{ccc}x=3\\y=-3\end{array}\right$