Lisa has $15 in her piggy bank. How much additional money does she need to buy a game that costs $75?

Solve the system of linear equations using the Gauss-Jordan elimination method. 2x + 3y 6212 3x + (x, y. z)

Gekata [30.6K]

Answer:

The solution of the system of linear equations is $x=3, y=4, z=1$

Step-by-step explanation:

We have the system of linear equations:

$2x+3y-6z=12\\x-2y+3z=-2\\3x+y=13$

Gauss-Jordan elimination method is the process of performing row operations to transform any matrix into reduced row-echelon form.

The first step is to transform the system of linear equations into the matrix form. A system of linear equations can be represented in matrix form (Ax=b) using a coefficient matrix (A), a variable matrix (x), and a constant matrix(b).

From the system of linear equations that we have, the coefficient matrix is

$\left[\begin{array}{ccc}2&3&-6\\1&-2&3\\3&1&0\end{array}\right]$

the variable matrix is

$\left[\begin{array}{c}x&y&z\end{array}\right]$

and the constant matrix is

$\left[\begin{array}{c}12&-2&13\end{array}\right]$

We also need the augmented matrix, this matrix is the result of joining the columns of the coefficient matrix and the constant matrix divided by a vertical bar, so

$\left[\begin{array}{ccc|c}2&3&-6&12\\1&-2&3&-2\\3&1&0&13\end{array}\right]$

To transform the augmented matrix to reduced row-echelon form we need to follow these row operations:

multiply the 1st row by 1/2

$\left[\begin{array}{ccc|c}1&3/2&-3&6\\1&-2&3&-2\\3&1&0&13\end{array}\right]$

add -1 times the 1st row to the 2nd row

$\left[\begin{array}{ccc|c}1&3/2&-3&6\\0&-7/2&6&-8\\3&1&0&13\end{array}\right]$

add -3 times the 1st row to the 3rd row

$\left[\begin{array}{ccc|c}1&3/2&-3&6\\0&-7/2&6&-8\\0&-7/2&9&-5\end{array}\right]$

multiply the 2nd row by -2/7

$\left[\begin{array}{ccc|c}1&3/2&-3&6\\0&1&-12/7&16/7\\0&-7/2&9&-5\end{array}\right]$

add 7/2 times the 2nd row to the 3rd row

$\left[\begin{array}{ccc|c}1&3/2&-3&6\\0&1&-12/7&16/7\\0&0&3&3\end{array}\right]$

multiply the 3rd row by 1/3

$\left[\begin{array}{ccc|c}1&3/2&-3&6\\0&1&-12/7&16/7\\0&0&1&1\end{array}\right]$

add 12/7 times the 3rd row to the 2nd row

$\left[\begin{array}{ccc|c}1&3/2&-3&6\\0&1&0&4\\0&0&1&1\end{array}\right]$

add 3 times the 3rd row to the 1st row

$\left[\begin{array}{ccc|c}1&3/2&0&9\\0&1&0&4\\0&0&1&1\end{array}\right]$

add -3/2 times the 2nd row to the 1st row

$\left[\begin{array}{ccc|c}1&0&0&3\\0&1&0&4\\0&0&1&1\end{array}\right]$

From the reduced row echelon form we have that

$x=3\\y=4\\z=1$

Since every column in the coefficient part of the matrix has a leading entry that means our system has a unique solution.

7 0

3 years ago

PLEASE HELP!!! A bridge has a weight limit of 5000 kg. What is the heaviest load that a pickup truck weighing 4500 pounds could

jeka57 [31]

Answer:

6500 lb

Step-by-step explanation:

The load limit of the bridge is ...

(5000 kg)(2.2 lb/kg) = 11,000 lb

The total of truck and trailer cannot exceed this value, so the trailer's weight cannot exceed ...

11,000 lb -4,500 lb = 6,500 lb . . . max trailer weight

5 0

3 years ago

20 points brainlist thanks

Fed [463]

Answer:

The answer Is 10.20

Step-by-step explanation:

d = \/(0-(-2))² + (-6-4)²

d = \/(0+2)² + (-10)²

d = \/(2² + 100)

d = \/(4+100)

d = \/104

d ~ 10,20

4 0

3 years ago

Read 2 more answers

You have 20 coins in your pocket that are either quarter or dimes. They total $3.95. How many quarters do you have? A.16 B.13 C.

bekas [8.4K]

Answer:

B. 13

Step-by-step explanation:

Solve this by setting up system of equations:

0.25x + 0.10y = 3.95

x + y = 20

x equals the number of quarters and y equals the number of dimes. 0.25 is the value of a quarter and 0.10 is the value of a dime.

1. Multiply one equation to have the same coefficient as the other

0.10 · (x + y = 20) = 0.10x + 0.10y = 2

2. Subtract to find the value of one variable

0.25x + 0.10y = 3.95

- 0.10x + 0.10y = 2

0.15x = 1.95

3. Solve for x by dividing both sides by 0.15

x = 13

3 0

3 years ago

Determine the intercepts of the line -5x-4y=10

Alexxandr [17]

Answer:

The y -intercept is: (0,−2.5)

The x -intercept is: (−2,0)

Step-by-step explanation:

7 0

3 years ago