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The sum of two number is 6. Twice the first number added to three times the second number is 10. Write a system of equations and

seropon [69]

Answer:

4 and 2 are the required numbers which satisfies the given equations

Step-by-step explanation:

Let the two numbers be x and y

According to the first condition

their is is 6

which is

x + y =6 ........................(i)

Now according to second condition

twice the first number i.e. 2x added to three time the second number i.e. 3y is 10

in form of equation it could be written as

2x + 3y = 10 ........................(ii)

Now from first equation we have

x + y =6

subtracting y from both sides

x = 6 - y .....................(iii)

Now putting this value of x in equation (ii)

equation (ii) is

2x + 3y = 10

Putting the value gives

2(6-y)+3y = 10

opening the brackets

12 - 2y + 3y = 10

12 - y = 10

subtracting 12 from both sides

12 - y -12 = 10 -12

it becomes

- y = -2

multiplying both sides by (-1)

it becomes

(-1)(-y) = (-2) * (-1)

y = 2

Now we got the value of y put it in equation iii which is

x = 6 -y

putting the value

x = 6 - 2

x = 4

So the two numbers are x = 4 and y = 2

3 0

3 years ago

Rewrite the system of linear equations as a matrix equation AX = B.

iren2701 [21]

Answer:

$\left[\begin{array}{ccc}1&2&5\\1&1&1\\4&6&5\end{array}\right]*\left[\begin{array}{ccc}x1\\x2\\x3\end{array}\right]=\left[\begin{array}{ccc}5\\6\\7\end{array}\right]$

Step-by-step explanation:

Let's find the answer.

Because we have 3 equations and 3 variables (x1, x2, x3) a 3x3 matrix (A) can be constructed by using their respectively coefficients.

Equations:

Eq. 1 : x1 + 2x2 + 5x3 = 5

Eq. 2 : x1 + x2 + x3 = 6

E1. 3 : 4x1 + 6x2 + 5x3 = 7

Coefficients for x1 ; x2 ; x3

From eq. 1 : 1 ; 2 ; 5

From eq. 2 : 1 ; 1 ; 1

From eq. 3 : 4 ; 6 ; 5

So matrix A is:

$\left[\begin{array}{ccc}1&2&5\\1&1&1\\4&6&5\end{array}\right]$

And the vector of vriables (X) is:

$\left[\begin{array}{ccc}x1\\x2\\x3\end{array}\right]$

Now we can find the resulting vector (B) using the 'resulting values' from each equation:

$\left[\begin{array}{ccc}5\\6\\7\end{array}\right]$

In conclusion, AX=B is:

$\left[\begin{array}{ccc}1&2&5\\1&1&1\\4&6&5\end{array}\right]*\left[\begin{array}{ccc}x1\\x2\\x3\end{array}\right]=\left[\begin{array}{ccc}5\\6\\7\end{array}\right]$

7 0

4 years ago

Lucy bought a couch that cost $1,000.00. she bought it using her debit card. She forgot she only has $900 in her checking accoun

expeople1 [14]

Answer:

4) overdraft fees

Step-by-step explanation:

if she now has a negative balance then she owes money to the couch store

8 0

3 years ago

Ella has 0.5 lbs of sugar. How much water should she add to make the following concentrations? Tell Ella how much syrup she will

olya-2409 [2.1K]

Answer:

1. 20% - add 2 lbs of water to get 2.5 lbs of syrup

2. 25% - add 1.5 lbs of water to get 2 lbs of syrup

3. 1.5% - add 32.833 lbs of water to get 33.333 lbs of syrup

Step-by-step explanation:

Ella has 0.5 lbs of sugar. Let x lbs be the amount of water Ella should add to get the syrup.

1. 20% syrup:

0.5 lbs - 20%

x+0.5 lbs - 100%

Write a proportion:

$\dfrac{0.5}{x+0.5}=\dfrac{20}{100}\\ \\0.5\cdot 100=(x+0.5)\cdot 20\\ \\50=20x+10\\ \\20x=50-10\\ \\20x=40\\ \\x=2\ lbs$

To get 20% syrup Ella should add 2 lbs of water. The total weight of strup is 2.5 lbs.

2. 25% syrup:

0.5 lbs - 25%

x+0.5 lbs - 100%

Write a proportion:

$\dfrac{0.5}{x+0.5}=\dfrac{25}{100}\\ \\0.5\cdot 100=(x+0.5)\cdot 25\\ \\50=25x+12.5\\ \\25x=50-12.5\\ \\25x=37.5\\ \\x=1.5\ lbs$

To get 25% syrup Ella should add 1.5 lbs of water. The total weight of strup is 2 lbs.

3. 1.5% syrup:

0.5 lbs - 1.5%

x+0.5 lbs - 100%

Write a proportion:

$\dfrac{0.5}{x+0.5}=\dfrac{1.5}{100}\\ \\0.5\cdot 100=(x+0.5)\cdot 1.5\\ \\50=1.5x+0.75\\ \\1.5x=50-0.75\\ \\1.5x=49.25\\ \\x=\dfrac{49.25}{1.5}\approx 32.833\ lbs$

To get 1.5% syrup Ella should add 32.833 lbs of water. The total weight of strup is 33.333 lbs.

7 0

3 years ago

What is 30 1/4% as a fraction?

DochEvi [55]

Answer:

7.5/30 or 25%

Step-by-step explanation:

30 x 0.25 = 7.5

7.5/30

7 0

3 years ago

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