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
Rasek [7]
3 years ago
10

Solve the system by using a matrix equation

Mathematics
2 answers:
Sergeu [11.5K]3 years ago
6 0

Answer:

Option A is correct (17,11).

Step-by-step explanation:

6x - 9y = 3

3x - 4y =7

it can be represented in matrix form as\left[\begin{array}{cc}6&-9\\3&4\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right] = \left[\begin{array}{c}3\\7\end{array}\right]

A= \left[\begin{array}{cc}6&-9\\3&4\end{array}\right]

X= \left[\begin{array}{c}x\\y\end{array}\right]

B= \left[\begin{array}{c}3\\7\end{array}\right]

i.e, AX=B

or X= A⁻¹ B

A⁻¹ = 1/|A| * Adj A

determinant of A = |A|= (6*-4) - (-9*3)

                                    = (-24)-(-27)

                                    = (-24) + 27 = 3

so, |A| = 3

Adj A=  \left[\begin{array}{cc}-4&9\\-3&6\end{array}\right]

A⁻¹ =  \left[\begin{array}{cc}-4&9\\-3&6\end{array}\right]/3

A⁻¹ =  \left[\begin{array}{cc}-4/3&3\\-1&2\end{array}\right]

X= A⁻¹ B

X=  \left[\begin{array}{cc}-4/3&3\\-1&2\end{array}\right] *\left[\begin{array}{c}3\\7\end{array}\right]

X= \left[\begin{array}{c}(-4/3*3) + (3*7)\\(-1*3) + (2*7)\end{array}\right]

X= \left[\begin{array}{c}-4+21\\-3+14\end{array}\right]

X= \left[\begin{array}{c}17\\11\end{array}\right]

x= 17, y= 11

solution set= (17,11).

SVETLANKA909090 [29]3 years ago
5 0

Answer:

a. (17,11)

Step-by-step explanation:

The given system is ;

6x-9y=3

3x-4y=7

The augmented matrices is

\left[\begin{array}{ccc}6&-9&|3\\3&-4&|7\end{array}\right]

Divide Row 1 by 6

\left[\begin{array}{ccc}1&-\frac{3}{2}&|\frac{1}{2}\\3&-4&|7\end{array}\right]

Subtract 3 times Row 1 from Row 2

\left[\begin{array}{ccc}1&-\frac{3}{2}&|\frac{1}{2}\\0&\frac{1}{2}&|\frac{11}{2}\end{array}\right]

Divide Row 2 by \frac{1}{2}

\left[\begin{array}{ccc}1&-\frac{3}{2}&|\frac{1}{2}\\0&1}&|11\end{array}\right]

Add \frac{3}{2} times Row 2 to Row 1

\left[\begin{array}{ccc}1&0&|17\\0&1}&|11\end{array}\right]

Hence the solution is (17,11)

You might be interested in
What is a rational number between -1/4 and 2/5
Sliva [168]
.20 is a rational number between -1/4 and 2/5.

It can be part of a ratio.

20:100

A fraction

20/100 or 1/5

I hope this helps!
~cupcake
4 0
3 years ago
→ PLEASE HELP ME! [99 POINTS] ←
zaharov [31]
B.

The cost for x children and y adults to go to the movies if adult tickets are $11 and child tickets are $6.

Example 3 children and 2 adults ( 6(3) + 11(2) )
5 0
3 years ago
Read 2 more answers
Mary is five times older than Julian. If the<br> sum of their ages is 42, how old is Mary?
Tanya [424]

Answer:

35

Step-by-step explanation:

M=5J

J=M/5

42=6J

42/6=7

Jullian is 7

7x5=35

Mary is 35

35+7=42

4 0
3 years ago
Read 2 more answers
16 of the 28 dogs at the shelter are purebred. What percent of the dogs are purebred? Round to a whole number
MArishka [77]

Answer:

57.14%

Step-by-step explanation:

So to get this answer I just had to find out what percent 16 was of 28. So 57.14% of the dogs are purebred.

3 0
3 years ago
Full-time ph.d. students receive an average of $12,837 per year with a standard deviation of $3000. find the probability that th
Ainat [17]
It is about 41.4% according to my TI-83/84 calculator.

7 0
2 years ago
Other questions:
  • Melton made 1 1/4 pounds of peanuts, 14 ounces of raisins, 12 ounces of walnuts, and 10 ounces of chocolate chips. If Milan divi
    14·1 answer
  • Solve for q, triangle ABC is similar to triangle JKL.​
    6·1 answer
  • Helppppp plz people!!!
    10·1 answer
  • Which of the following statements is not true?
    9·1 answer
  • How many four letter passwords can be created if no repetition is allowed?
    13·1 answer
  • A rectangle is to be inscribed in a right triangle having sides of length 66in, 88in, and 110in. Find the dimensions of the rect
    14·1 answer
  • I need help!!! asapWhat is the ratio as you change from B to A?
    7·1 answer
  • Help i am stuck please be fast
    14·1 answer
  • * Which expression is equivalent to 7(p + 5) *​
    7·1 answer
  • Why do some people sleep with hair rollers
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!