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Sagot :
Answer:
(3, -3)
Step-by-step explanation:
METHOD 1.
Put the coordinates of the given points to the equations and check the equality.
[tex]\left\{\begin{array}{ccc}y=3x-12&(1)\\4x+6y=-6&(2)\end{array}\right[/tex]
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:
[tex]\left\{\begin{array}{ccc}y=3x-12&(1)\\4x+6y=-6&(2)\end{array}\right[/tex]
substitute (1) to (2):
[tex]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}[/tex]
put it to (1):
[tex]y=3(3)-12\\y=9-12\\\boxed{y=-3}[/tex]
[tex]\left\{\begin{array}{ccc}x=3\\y=-3\end{array}\right[/tex]
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