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3 years ago

Find the solution set (x,y,z) of the system: 3x-2y+4z=6 2y-3z=20 6z=12

Mathematics

1 answer:

gizmo_the_mogwai [7]3 years ago

4 0

Answer:

The solution is x = 8, y = 13 and z = 2.

Step-by-step explanation:

We are given a system of equations with the variables x, y, and z from which we have to solve for x, y, and z.

The equations are

3x - 2y + 4z = 6 ........ (1)

2y - 3z = 20 .......... (2)

6z = 12 ......... (3)

Now, from equation (3), we get z = 2.

Now, putting z = 2 in equation (2) we get

2y = 20 + 6 = 26

⇒ y = 13

Now, from equation (1), putting y = 13 and z = 2, we get

3x = 6 - (4 × 2) + (2 × 13) = 24

⇒ x = 8

So the solution is x = 8, y = 13 and z = 2. (Answer)

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Option A:

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Solution:

Given expression is 6 – 4(3) ____ 5 – 10.

Let us first simplify the expression.

Take left side expression.

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Take right side expression.

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Step-by-step explanation:

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Answer:

Part a) The variables are

x (the number of packages of Twinkies that were sold)

y (the number o boxes of juice that were sold)

Part b) The system of equations is

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Part c) $x=37,y=42$

Part d) The value of y represent the number of boxes of juice that were sold $y=42\ boxes\ of\ juice$

The value of x represent the number of packages of Twinkies that were sold $x=37\ packages\ of\ Twinkies$

Step-by-step explanation:

Part a) Define the variables in this situation

Let

x-----> the number of packages of Twinkies that were sold

y----> the number of boxes of juice that were sold

Part b) Write a system of equations that model the problem

we know that

$x+y=79$ ------> equation A

$1.65x+1.36y=118.17$ ---> equation B

Part c) Use the linear combination method to find the solution to the system you wrote in part b

Multiply equation A by -1.65

$-1.65(x+y)=-1.65*79$

$-1.65x-1.65y=-130.35$ ------> equation C

Adds equation C and equation B

$-1.65x-1.65y=-130.35\\1.65x+1.36y=118.17\\---------\\-1.65y+1.36y=-130.35+118.17\\-0.29y=-12.18\\y=42$

Find the value of x

$x+y=79$

$x+42=79$

$x=79-42=37$

Part d) Using a complete sentence, explain what the solution found in part c represents

The value of y represent the number of boxes of juice that were sold

$y=42\ boxes\ of\ juice$

The value of x represent the number of packages of Twinkies that were sold

$x=37\ packages\ of\ Twinkies$

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