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
Aleks [24]
3 years ago
6

Solve the system. If there is more than one solution, write the general solution. x + y - 2z = 9 3x + y + 2z = 15 x - 5y + 22z =

-27 Solution {-2z + 3, 4z + 6, z | z is any real number}
Mathematics
1 answer:
Margaret [11]3 years ago
7 0

Answer:

<h2>x = (12-k)/2, y = k, z = (k-6)/4 </h2>

Step-by-step explanation:

Given the system of equation

x + y - 2z = 9 ... 1

3x + y + 2z = 15 ...2

x - 5y + 22z = -27... 3

First let us reduce the system of equation into two with two unknowns.

Subtracting 1 from 3

y-(-5y) + (-2z-22z) = 9-(-27)

y+5y + (-24z) = 9+27

6y-24z = 36 ... 4

Multiplying equation 1 by 3 and subtracting from equation 2

3x + 3y - 6z = 27

3x + y + 2z = 15

On subtracting both;

(3y-y)+(-6z-2z) = 27-15

2y-8z = 12 ... 5

Equating 4 and 5

6y-24z = 36 ... 4

2y-8z = 12 ... 5

Multiplying equation 5 by 3 the equation becomes;

6y-24z = 36 ... 6

6y-24z = 36 ... 7

We can see that equation 6 and 7 are the same;

let y = k

6k - 24z = 36

k - 4z = 6

4z = k-6

z = k-6/4

Substituting y = k and z = k-6/4 into equation 1 to get x

From 1; x + y - 2z = 9 ... 1

x + k -2( k-6/4) = 9

x + k - (k-6)/2 = 9

x = 9+(k-6)/2-k

x = {18+(k-6)-2k}/2

x = (12-k)/2

The solutions to the system of equations are x = (12-k)/2, y = k, z = (k-6)/4 where k is any constant. This shows that the system of equation has infinite solutions.

You might be interested in
Find the product. (a2 + 2a + 1)(a + 1) a. A2 + 3a + 2 b. A3 + 3a2 + 3a + 1 c. A3 + 2a 2 + a + 1 d. A3 + 3a2 + a + 1
olchik [2.2K]

 (a + 1)(a² + 2a + 1)

= a(a² + 2a + 1) + 1(a² + 2a + 1)

= a³ + 2a² + a   + a² + 2a + 1

= a³ + 3a² + 3a + 1

Answer: b

7 0
3 years ago
Find the length of side x in simplest radical form with a rational denominator.
kogti [31]

Answer:

since it is Right angled isosceles triangle it's base side are equal

by using Pythagoras law

x²+x²=1²

2x²=1

x=√{1/2}or 0.707 or 0.71

6 0
3 years ago
A plane is an undefined term because it
igor_vitrenko [27]
No on can explain it but it has a definition.
8 0
3 years ago
Which graph represents the function f(x)=4*3^x (f times x equals 4 times three to the power of x)
pychu [463]

Answer:

The answer to your question is the first graph in the second line.

Step-by-step explanation:

First graph in the first line: it shows a positive graph that intercepts the y-axis in 5, then this graph is not the correct answer.

Second graph in the first line: it shows a negative graph, this option is incorrect, we look for a positive graph.

First graph in the second line: is correct because is a positive graph and intercpts the y-axis in 4.

Second graph in the second line: is incorrect although it is a positive graph, it intercepts the y-axis in 3.

7 0
3 years ago
Match the measures with the correct type of measurement. a.72m b. 125mm3 c. 50cm2 Volume, Surface Area, Perimeter​
Lesechka [4]

a. Perimeter

b. Volume

c.Suface Area

5 0
3 years ago
Other questions:
  • A cone is a polyhedron with a circular base.<br> true or false?
    7·2 answers
  • S a punishment for something naughty that we did, my little brother and I have to whitewash both sides of a fence. We start at t
    7·1 answer
  • Choose the fraction that is equal to:
    10·2 answers
  • Please answer this multiple choice question correctly for 30 points and brainliest!!
    11·1 answer
  • How many times can 20 go into 98 with a two digit number
    12·2 answers
  • Which animal traveled at a rate of 1.5 meters per minute?
    11·2 answers
  • By what least number should 2048 be multiplied to get a perfect cube
    13·2 answers
  • If Margo has about 120,000 balloons to blow up for the fair, and she's already blown up 146, how many more balloons does she nee
    8·1 answer
  • in one day a movie rented out 35 comedies. If the ratio of comedies rented action movies rented was 5:2 how many action movies w
    9·1 answer
  • Write the equation in slope-intercept form through the point (-4, -7) and is perpendicular to the line y = -(7/4)x + 4 and graph
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!