-5x2(2) + (-2)(2) what is the answer

Apply Crammer's Rule to find the solution to the following quations .2x + 3y = 1, 3x + y = 5

Bond [772]

Answer:

The solution to the equation system given is:

<u>x = 2</u>
<u>y = -1</u>

Step-by-step explanation:

First, we must know the equations given:

2x + 3y = 1
3x + y = 5

Following Crammer's Rule, we have the matrix form:

$\left[\begin{array}{ccc}2&3\\3&1\end{array}\right] =\left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}1\\5\end{array}\right]$

Now we solve using the determinants:

$x=\frac{\left[\begin{array}{ccc}1&3\\5&1\end{array}\right]}{\left[\begin{array}{ccc}2&3\\3&1\end{array}\right] } =\frac{(1*1)-(5*3)}{(2*1)-(3*3)} = \frac{1-15}{2-9} =\frac{-14}{-7} = 2$

$y=\frac{\left[\begin{array}{ccc}2&1\\3&5\end{array}\right]}{\left[\begin{array}{ccc}2&3\\3&1\end{array}\right] } =\frac{(2*5)-(3*1)}{(2*1)-(3*3)}=\frac{10-3}{2-9} =\frac{7}{-7}=-1$

Now, we can find the answer which is x= 2 and y= -1, we can replace these values in the equation to confirm the results are right, with the first equation:

2x + 3y = 1
2(2) + 3(-1)= 1
4 - 3 = 1
1 = 1

And, with the second equation:

3x + y = 5
3(2) + (-1) = 5
6 - 1 = 5
5 = 5

4 0

2 years ago

For each value of U, determine whether it is a solution,

abruzzese [7]

Given u/7 - 1 = 7 and plugging in values for u,

For u = 28; 28/7 - 1 = 4 - 1 = 3; No
For u = -49; -49/7 - 1 = -7 - 1 = -8; No
For u = 42; 42/7 - 1 = 6 - 1 = 5; No
For u = 0; 0/7 - 1 = -1; No

Another way to find out which value would be a solution to u/7 - 1 = 7 is to solve for u.

u/7 - 1 = 7
u/7 = 7 + 1
u/7 = 8
u = 8*7
u = 56

The only solution to this equation is when u = 56.

8 0

2 years ago

Marc ordered a rug. He gave a deposit of 30% of the cost and will pay the rest when the rug is delivered. If the deposit was $75

ra1l [238]

Answer: Marc still owes $175

Step-by-step explanation:

Let x represent the cost of the rug.

Marc ordered a rug and gave a deposit of 30% of the cost and will pay the rest when the rug is delivered. This means that the amount of money that he deposited

for the rug is

30/100 × x = 0.3 × x = 0.3x

If the deposit was $75, it means that

0.3x = 75

x = 75/0.3 = 250

The cost of the rug is $250

The amount that Marc still owes would be

250 - 75 = $175

6 0

2 years ago

The third term of an arithmetic sequence is 14 and the 9th term is -1. Find the first four terms of the sequence.

Liula [17]

Answer:

The first four terms of the sequence are : 19, 16.5 , 14 , 11.5

Step-by-step explanation:

In the given sequence:

a(3) = 14, a(9) = -1

The general term of a sequence in Arithmetic Progression is:

a(n) = a + (n-1)d

a(3) = a + (3 -1) d = a + 2 d

and a(9) = a + (9- 1 ) d = a + 8 d

⇒ a + 2 d = 14 ......... (1)

and a + 8 d = -1 ........... (2)

Now, solving the given system of equation, we get:

From (1), a = 14 - 2 d

Put in (2), we get:

a + 8 d = -1 ⇒ 14 - 2 d + 8d = -1

⇒ 14 + 6d = -1

or, 6d = -1 -14 = -15

⇒ d = -15/6 = -2.5

or, d = -2.5

Then a = 14 - 2 d = 14 - 2(-2.5) =14 + 5 = 19, or a = 19

Now, first four terms of the sequence is:

a = 19

a(2) = a + 4 = 19 - 2.5 = 16.5

a(3) = a + 2d = 19 + 2(-2.5) = 19 - 5 = 14

a(4) = a + 3d = 19 + 3(-2.5) = 19 - 7.5 = 11.5

Hence, the first four terms of the sequence are : 19, 16.5 , 14 , 11.5

4 0

2 years ago

Free cheat!!!!division!!

In-s [12.5K]

Answer:

3/2 3*5=15

3/2=1.5

Step-by-step explanation:

8 0

2 years ago