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3 years ago

What is the solution of the system of equations? -y+3x=6 y=-6x+12

Mathematics

2 answers:

irinina [24]3 years ago

8 0

Answer:

x = 2

y = 0

Step-by-step explanation:

We can solve using substitution, substitute y in the first equation with the second equation:

-(-6x + 12) + 3x = 6

Distribute the negative sign:

6x - 12 + 3x = 6

Combine like terms:

9x - 12 = 6

Isolate the variable and solve for x by adding 12 in both sides:

9x = 18

x = 2

Substitute 2 with x in any equation to find the value of y:

-y + 3(2) = 6

-y + 6 = 6

Subtract 6 in both sides to isolate the variable:

-y = 0

0/-1 = 0

y = 0

Our answer would be x = 2 and y = 0

Nady [450]3 years ago

7 0

Answer:

(2,0)

Step-by-step explanation:

I'm going to use substitution since one of the variables in one of the equation is already solved for.

-y+3x=6

y=-6x+12

I'm going to replace the first y with the second y which is (-6x+12).

This gives me:

-(-6x+12)+3x=6

Distribute:

6x-12+3x=6

Combine like terms:

9x-12=6

Add 12 on both sides:

9x=18

Divide both sides by 9:

x=2

If x=2 and y=-6x+12, then y=-6(2)+12=-12+12=0.

The solution (the intersection) is (2,0).

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Answer:

A. 0.16

B. 0.58

C. No

D. Dependent

Step-by-step explanation:

The sampling space has 36 outcomes.

The event A has 6 outcomes (3,1), (3,3), (3,5), (4,1), (4,3),(4,5)

So P(A)= 6/36 = 0.16

The table in the picture shows the 15 outcomes that are not allowed, so there are 36-15 = 21 possible outcomes for B and its probability is 21/36 = 0.58

Are A and B mutually exclusive events?

No since their intersection is not empty, for example (3,1) belongs to both A and B

In order for A and B to be independent, it must happen that

P(A∩B)=P(A)P(B)

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whereas

P(A)P(B) = (6/36)(21/36) = (1/6)(7/12)=7/72

So A and B are not independent.

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