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3 years ago

How many solutions does the system of equations have 3x = -12y + 15 and x + 4y = 5

2 answers:

6 0

Below are the answers:

1. 3x = - 12y + 15 3x + 12y = 15 reduces to x + 4y = 5 this matches the other equation, therefore, they are on the same line and have INFINITE SOLUTIONS
2. y = 6x + 2 -6x + y = 2 6x - y = -2 3y - 18x = 12 -18x + 3y = 12 18x - 3y = -12 reduces to 6x - y = -4 The equations do not match, therefore, there is NO SOLUTION
3. x - 4y = 12 5x - 20y = 60 reduces to x - 4y = 12 same equation, same line, INFINITE SOLUTIONS
4. y - 6x = -3 -6x + y = -3 6x - y = 3
4y - 24x = -16 -24x + 4y = -16 24x - 4y = 16 reduces to 6x - y = 4
NO SOLUTIONS

lara [203]3 years ago

4 0

Answer:

Part 1) Infinite solutions

Part 2) No solutions

Part 3) Infinite solutions

Part 4) No solutions

Step-by-step explanation:

Part 1) we have

$3x=-12y+15$

Group the variables

$3x+12y=15$ -------> equation A

$x+4y=5$ -------> equation B

Multiply by $3$ equation B

$3*(x+4y)=3*5$ ------> $3x+12y=15$

The equation A and the equation B are the same equation, is the same line

therefore

The system has infinite solutions

Part 2) we have

$y=6x+2$ -------> equation A

$3y-18x=12$

Isolate the variable y

$3y=18x+12$ ------> Divide by $3$ both sides

$y=6x+4$ -------> equation B

we know that

If two lines has the same slope , then they are parallel lines

In this problem the line of the equation A and the line of the equation B has the same slope $m=6$

therefore

Line A and Line B are parallel lines

The system has no solution

Part 3) we have

$x-4y=12$ -------> equation A

$5x-20y=60$ -------> equation B

Multiply by $5$ equation A

$5*(x-4y)=5*12$ -------> $5x-20y=60$

The equation A and the equation B are the same equation, is the same line

therefore

The system has infinite solutions

Part 4) we have

$y-6x=-3$

Isolate the variable y

$y=6x-3$ -------> equation A

$4y-24x=-16$

Isolate the variable y

$4y=24x-16$ ------> Divide by $4$ both sides

$y=6x-4$ -------> equation B

we know that

If two lines has the same slope , then they are parallel lines

In this problem the line of the equation A and the line of the equation B has the same slope $m=6$

therefore

Line A and Line B are parallel lines

The system has no solution

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3 years ago

When an automobile is stopped with a roving safety patrol,each tire is checked for tire wear, and each headlight is checkedto se

ryzh [129]

Answer:

a) Joint ptobability distribution

$\begin{pmatrix} &Y=0&Y=1&Y=2&Y=3&Y=4\\X=0&0.3&0.05&0.025&0.025&0.1\\ X=1&0.18&0.03&0.015&0.015&0.06 \\ X=2&0.12&0.02&0.01&0.01&0.04\end{pmatrix}$

b) P(X<= 1 and Y <= 1) = P(X<= 1) * P(Y<=1) = 0.56

c) P(X + Y = 0)=0.3

d) P(X + Y <= 1)=0.53

Step-by-step explanation:

We have to construct the joint probability table with the marginal probabilities of X and Y.

X can take values from 0 to 2, and Y can take values from 0 to 4.

We can calculate each point of the joint probability as:

$P(x,y)=P_x(x)*P_y(y)$

Then, the joint probabilities are:

X=0 Y=0 Px=0.5 Px=0.6 P(0,0)=0.3

X=0 Y=1 Px=0.5 Px=0.1 P(0,1)=0.05

X=0 Y=2 Px=0.5 Px=0.05 P(0,2)=0.025

X=0 Y=3 Px=0.5 Px=0.05 P(0,3)=0.025

X=0 Y=4 Px=0.5 Px=0.2 P(0,4)=0.1

X=1 Y=0 Px=0.3 Px=0.6 P(1,0)=0.18

X=1 Y=1 Px=0.3 Px=0.1 P(1,1)=0.03

X=1 Y=2 Px=0.3 Px=0.05 P(1,2)=0.015

X=1 Y=3 Px=0.3 Px=0.05 P(1,3)=0.015

X=1 Y=4 Px=0.3 Px=0.2 P(1,4)=0.06

X=2 Y=0 Px=0.2 Px=0.6 P(2,0)=0.12

X=2 Y=1 Px=0.2 Px=0.1 P(2,1)=0.02

X=2 Y=2 Px=0.2 Px=0.05 P(2,2)=0.01

X=2 Y=3 Px=0.2 Px=0.05 P(2,3)=0.01

X=2 Y=4 Px=0.2 Px=0.2 P(2,4)=0.04

We can write it in the form of a matrix:

$\begin{pmatrix} &Y=0&Y=1&Y=2&Y=3&Y=4\\X=0&0.3&0.05&0.025&0.025&0.1\\ X=1&0.18&0.03&0.015&0.015&0.06 \\ X=2&0.12&0.02&0.01&0.01&0.04\end{pmatrix}$

b) From the joint probability P(X<= 1 and Y <= 1) is equal to

$P(X\leq 1 \& Y \leq 1)=P(0,0)+P(0,1)+P(1,0)+P(1,1)\\\\P(X\leq 1 \& Y \leq 1)=0.3+0.05+0.18+0.03=0.56$

We can calculate P(X<= 1) * P(Y<=1)

$P_x(X\leq 1)=P_x(0)+P_x(1)=0.5+0.3=0.8\\\\P_y(Y\leq1)=P_y(0)+P_y(1)=0.6+0.1=0.7\\\\P_x(X\leq1)*P_y(Y\leq1)=0.8*0.7=0.56$

Both calculations give the same result.

c) Probability of no violations

$P(X+Y=0)=P(0,0)=0.3$

d) P(X + Y <= 1)

$P(X+Y \leq 1)=P(0,0)+P(0,1)+P(1,0)\\\\P(X+Y \leq 1)=0.3+0.05+0.18=0.53$

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3 years ago

Which of the following equations is equivalent to x - y = 5?

Masja [62]

Answer:

$6x-6y=30$

Step-by-step explanation:

The complete options are

a) x - 2y = 30

b) 4x - 3y = 30

c) 3x - 4y = 30

d) 6x - 6y = 30

The given equation is

$x-y=5$

Verify option d

we have

$6x-6y=30$

Divide by 6 both sides

$(6x-6y)/6=30/6$

$\frac{6x}{6}-\frac{6y}{6}=\frac{30}{6}$

$x-y=5$

therefore

$x-y=5$ and $6x-6y=30$ are equivalent

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3 years ago

Simplify x + 6.2 + 8.5. 6.2x + 8.5 x + 14.7 0 14.7×

Alenkinab [10]

Answer:

x + 14.7

Step-by-step explanation:

Simply combine like terms. Constants go with each other and x terms go with each other.

6.2 + 8.5 = 14.7

x = x

x + 14.7

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Step-by-step explanation:

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