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
vlabodo [156]
3 years ago
12

Solve the system by using a matrix equation. --4x - 5y = -5 -6x - 8y = -2

Mathematics
1 answer:
evablogger [386]3 years ago
4 0

Answer:

Solution : (15, - 11)

Step-by-step explanation:

We want to solve this problem using a matrix, so it would be wise to apply Gaussian elimination. Doing so we can start by writing out the matrix of the coefficients, and the solutions ( - 5 and - 2 ) --- ( 1 )

\begin{bmatrix}-4&-5&|&-5\\ -6&-8&|&-2\end{bmatrix}

Now let's begin by canceling the leading coefficient in each row, reaching row echelon form, as we desire --- ( 2 )

Row Echelon Form :

\begin{pmatrix}1\:&\:\cdots \:&\:b\:\\ 0\:&\ddots \:&\:\vdots \\ 0\:&\:0\:&\:1\end{pmatrix}

Step # 1 : Swap the first and second matrix rows,

\begin{pmatrix}-6&-8&-2\\ -4&-5&-5\end{pmatrix}

Step # 2 : Cancel leading coefficient in row 2 through R_2\:\leftarrow \:R_2-\frac{2}{3}\cdot \:R_1,

\begin{pmatrix}-6&-8&-2\\ 0&\frac{1}{3}&-\frac{11}{3}\end{pmatrix}

Now we can continue canceling the leading coefficient in each row, and finally reach the following matrix.

\begin{bmatrix}1&0&|&15\\ 0&1&|&-11\end{bmatrix}

As you can see our solution is x = 15, y = - 11 or (15, - 11).

You might be interested in
Ashlyn is selling boxes of cookies for a fundraiser. If she raised $26 selling eight boxes, how much will she raise if she sells
allochka39001 [22]
She raises thirteen dollars
6 0
3 years ago
Read 2 more answers
Behavior patterns which are already present at birth are called ____
PIT_PIT [208]

Answer:

instincts

Step-by-step explanation:

i luv u!

7 0
2 years ago
Charles will babysit for up to 4 hours and charges $7 per hour. Write a function in function notation for this situation.
Sloan [31]
X hour and 7 dollars per hour

x = hour

7(x) is your function


thank you for Anlian for pointing it out.. there is 4 hours

so x = 4

plug in 4 in x. 7(4)

7 x 4 = 28

28 is your answer

hope this helps
6 0
3 years ago
Read 2 more answers
PLEASE HELP 25PT
Bess [88]
Hi


1.If Mrs.Walters drives 360 miles on 25 gallons of gas , she drives 14.4 miles on 1 gallon of gas .

Work; I made a proportion , but you can just divide 360 and 25 .
 x=14.4 miles

If Mr.Walters drives 480 miles on 32 gallons of gas , he drives 15.06 miles on 1 gallon of gas .
 x=15.06 miles
2. Mr.Walter because he drives more miles with a gallon .
Work; 15.06 miles is greater than 14.4 miles.

Hope it helps and have a wonderful day.
7 0
3 years ago
Intrigued by a 2013 study at the University of Nebraska that suggested marijuana smokers may be thinner than other adults, a gro
Reptile [31]

this question is incomplete, the complete question is:

1. is this model effective

2. what is the correlation coefficient for this data.

3. for a student with a bmi of 25, what is the predicted number of hours under the influence.

Step-by-step explanation:

1. first of all this model is not effective because we have r² as 0.134. this tells us that only 13.4 percent of the of the variations that exist in this data has been explained by the model

1. we get the correlation coefficient by

+-\sqrt{r^{2} }

the regression slope coefficient has a negative sign. this is what we would use in calculating the correlation coefficient.

-\sqrt{r^{2} }

= -√0.134

= -0.366

therefore the correlation coefficient is -0.366

2. to get the number of hours under the influence with a bmi of 25

the equation is

49.2-1.15bmi

= 49.2-1.15(25)

= 49.2-28.75

= 20.45

8 0
3 years ago
Other questions:
  • A train travels at a constant speed of 35 mi/h.
    8·1 answer
  • Help!
    5·2 answers
  • 1. Molina is sewing a border of ribbon onto her rectangular picnic blanket. The long side of the blanket is 7 feet and the short
    14·1 answer
  • If the measure of 0 is A radians and B degrees, then A=180B/pie
    14·1 answer
  • For this problem, assume Gwen and Harry have 5 types of cones and 9 flavors of ice cream.
    8·1 answer
  • Which problem can be solved using the equation below?<br> 36 : 4=
    8·1 answer
  • PLEASE ANSWER I HAVE ONLY A FEW HOURS LEFT!!!!!!!!!!
    6·1 answer
  • Your recipe for muffins says you have to 3 times as many blueberries than strawberries. Write an expression for the situation. N
    14·1 answer
  • Find the missing angles
    9·1 answer
  • PLEASE HELP
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!