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asambeis [7]
2 years ago
5

What is the solution to the following system?

Mathematics
1 answer:
Rainbow [258]2 years ago
5 0

The solutions are x = 1, y = -3, z = 1 after solving with substitution method option second x= 1, y=-3, z = 1 is correct.

<h3>What is a linear equation?</h3>

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have three linear equations in three variable:

4x + 3y - z = -6 ..(1)

6x - y+ 3z = 12 ..(2)

8x + 2y + 4z = 6 ...(3)

From the equation (1)

\rm x=\dfrac{-6-3y+z}{4}

Substitute the above value in the equation (2) and (3):

\rm 6\cdot \dfrac{-6-3y+z}{4}-y+3z=12\\\\ 8\cdot \dfrac{-6-3y+z}{4}+2y+4z=6

After simplification:

\rm -11y+9z-18=24\\ -4y+6z-12=6

After solving the above two equations by substitution method:

z = 1

y = -3

Plug the above two values in the equation (1), we get:

x = 1

Thus, the solutions are x = 1, y = -3, z = 1 after solving with substitution method option second x= 1, y=-3, z = 1 is correct.

Learn more about the linear equation here:

brainly.com/question/11897796

#SPJ1

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What algebraic expression could represent the average of 2x, x + 3, and 6x?
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Answer:

(5x = 2 = 3 +8a

Step-by-step explanation:

8 0
3 years ago
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During a bike challenge riders have to collect various colored ribbons each half mile they collect a red ribbon each 8th mile th
soldi70 [24.7K]

Answer:

Green and Blue ribbon

Step-by-step explanation:

Given

They collect

Red Ribbon = ½ mile

Green Ribbon = ⅛ mile

Blue Ribbon = ¼ mile

To find?

Which colors of ribbons will be collected at the ¾ mile mark.

The interpretation of the question is to test which of the above fractions can divide ¾ without a remainder; in other words, multiples of ¾.

Testing each fraction.

Red Ribbon = ½

¾ ÷ ½

= ¾ * 2

= 3/2

= 1.5 or 1 Remainder 1

This is not an exact multiple of ¾. So, the red ribbon won't be passed here.

Green Ribbon = ⅛

¾ ÷ ⅛

= ¾ * 8

= 24/8

= 3

This is an exact multiple of ¾. So, the green ribbon will be collected.

Testing the last ribbon

Blue = ¼

¾ ÷ ¼

= ¾ * 4

= 3

This is an exact multiple of ¾. So, the blue ribbon will be collected.

Hence, the green and blue ribbons will be collected at ¾ mile mark

3 0
3 years ago
A bakery wants to determine how many trays of doughnuts it should prepare each day. Demand is normal with a mean of 5 trays and
Alexeev081 [22]

Answer:

4 trays should he prepared, if the owner wants a service level of at least 95%.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 5

Standard Deviation, σ = 1

We are given that the distribution of demand score is a bell shaped distribution that is a normal distribution.

Formula:

z_{score} = \displaystyle\frac{x-\mu}{\sigma}

P(X > x) = 0.95

We have to find the value of x such that the probability is 0.95

P(X > x)  

P( X > x) = P( z > \displaystyle\frac{x - 5}{1})=0.95  

= 1 -P( z \leq \displaystyle\frac{x - 5}{1})=0.95  

=P( z \leq \displaystyle\frac{x - 5}{1})=0.05  

Calculation the value from standard normal z table, we have,  

\displaystyle\frac{x - 5}{1} = -1.645\\x = 3.355 \approx 4  

Hence,  4 trays should he prepared, if the owner wants a service level of at least 95%.

3 0
3 years ago
Keylee writes the equation 6x+12=2(3x+6), Can you find the number of solutions this equation has without solving for x? Explain
Natasha2012 [34]

Answer:

All Real Numbers Are The Solutions

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3 years ago
What kind of association is this, negative or positive?​
erik [133]

Answer:

negative association

Step-by-step explanation:

This diagram is a scatter plot which represents a set of data.  Data on a scatter plot can fit one of three descriptions:  positive (increasing), negative (decreasing) or no association (points do not form any kind of line).  Given this data and the line of best fit, or the line that pass through the majority of the points, it is a decreasing line.  Since the line goes downhill, it is a negative association.  

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3 years ago
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