1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
saveliy_v [14]
2 years ago
15

Given the system of equations: 2x – y = –2 x = 14 + 2y What is the value of the system determinant? What is the value of the y−d

eterminant? What is the value of the x−determinant? What is the solution to the system of equations?
Mathematics
2 answers:
lbvjy [14]2 years ago
8 0

<u>ANSWER 1</u>

The given system  of equations is:

2x-y=-2

x=14+2y

Let us rewrite the second system to obtain,

2x-y=-2

x-2y=14

We need to apply the Cramer's rule. So we write out the coefficient matrices to obtain:

\left[\begin{array}{cc}2&-1\\1&-2\end{array}\right]


The answer column is;

\left[\begin{array}{c}-2&14\end{array}\right]


The value of the y-determinant is denoted by D_y. To find this we replace the coefficient determinant with answer-column values in y-column to get,

D_y=\left|\begin{array}{cc}2&-2\\1&14\end{array}\right|

Recall that,

If A=\left[\begin{array}{cc}a&b\\c&d\end{array}\right]

then, det_{A}=\left|\begin{array}{cc}a&b\\c&d\end{array}\right|=ad-bc

This implies that,

D_y=2\times14-1\times(-2)

D_y=28+2

D_y=30


<u>ANSWER 2</u>

The value of the x-determinant is denoted by D_x. To find this we replace the coefficient determinant with answer-column values in x-column to get,

D_x=\left|\begin{array}{cc}-2&-1\\14&-2\end{array}\right|


This implies that,

D_x=-2\times-2-14\times-1

D_x=4+14

D_x=18


<u>ANSWER 3</u>

To find the solution to the system of equations.


We need to find the determinant of the coefficient matrix.

D=\left|\begin{array}{cc}2&-1\\1&-2\end{array}\right|


This implies that,

D=2\times(-2)-1\times-1


D=-4+1


D=-3


Cramer's rule says that,

x=\frac{D_x}{D}


\Rightarrow x=\frac{18}{-3}


\Rightarrow x=-6


and


y=\frac{D_y}{D}


\Rightarrow y=\frac{30}{-3}


\Rightarrow y=-10


Therefore the solution is x=-6 and  y=-10.

sineoko [7]2 years ago
4 0
2x - y = -2

x = 14 + 2y

Plug in the x equation

2(14+2y) - y = -2

Distribute

28 + 4y - y = -2

Combine variables

28 + 3y = -2

Subtract 28 on both sides

3y = -30

Divide the y

y = -10

You might be interested in
88.83 is what percent of 21
Serjik [45]

88.83 / 21  =  4.23

4.23  is the same number as  423% .

8.23  is  <em>423%</em>  of  21.
6 0
2 years ago
Read 2 more answers
80% of Vanessa's final grade is based on the average score of her quizzes, which is 73.
Misha Larkins [42]
80% of quizzes + 20% of final = final grade

80% * 73 + 20% * x = 70

0.8 * 73 + 0.2x = 70

58.4 + 0.2x = 70

0.2x = 11.6

x = 58
8 0
3 years ago
About how many meters is a 40-yard race
Varvara68 [4.7K]

Answer:

36.576 meters or 36.58 meters

Step-by-step explanation:


5 0
3 years ago
Cost of article = $455 Percentage of markup (on cost) = 28%
SpyIntel [72]
The cost would be $582.40!

I hope this helped! Mark me Brainliest! :) -Raven❤️
5 0
2 years ago
Pls help will give brainlest.
Arada [10]

2,400 in.³

I Love Maths :)

7 0
2 years ago
Read 2 more answers
Other questions:
  • Please need with one
    7·1 answer
  • An accountant needs to withhold 18% of income for taxes if the income is below $40,000, and 27% of income if the income is $40,0
    10·1 answer
  • Is this a dilation if it’s turned?
    14·2 answers
  • A theatre costs £63 plus a booking fee of 3%
    11·1 answer
  • Which expression is equivalent to (124)29?(124)29?​
    5·2 answers
  • Imagine that you're on a game show, and you're given the choice of a mystery prize behind one of three doors: Behind one door is
    7·1 answer
  • Simplify the expression: show all ur steps/ wrk PLEASE,1+2x3-18/3+(5(2+2)]
    10·2 answers
  • What is the answer?
    12·1 answer
  • HELPPPPPPPPPPPPPP MEEEEEEEEEEEEEE
    11·2 answers
  • This equation shows how the number of cookies Jonah can bake is related to the amount of flour he has. c = 8f The variable f rep
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!