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
mina [271]
2 years ago
14

Solve the system 6x -2y+z= -2 2x+ 3y - 3z =11 x+ 6y=31

Mathematics
1 answer:
weqwewe [10]2 years ago
8 0

Answer:

x = 1

y = 5

z = 2

Step-by-step explanation:

System of equations:

6x - 2y + z = -2

2x + 3y - 3z = 11

x + 6y = 31

Isolate one variable in any of the equations:

x + 6y = 31

x = 31 - 6y

Plug in this value for x in another equation:

6(31 - 6y) - 2y + z = -2

186 - 36y - 2y + z = -2

186 - 38y + z = -2

-38y + z = -188

z = -188 + 38y

Plug in these values in the remaining equation:

2(31 - 6y) + 3y - 3(-188 + 38y) = 11

62 - 12y + 3y + 564 - 114y = 11

626 - 12y + 3y - 114y = 11

626 - 9y - 114y = 11

626 - 123y = 11

-123y = -615

y = 5

Plug in value of y into our other answers to solve for x and z:

x = 31 - 6(5)

x = 31 - 30

x = 1

z = -188 + 38(5)

z = -188 + 190

z = 2

Check your work:

6x - 2y + z = -2

6(1) - 2(5) + 2 = -2

6 - 10 + 2 = -2

-4 + 2 = -2

-2 = -2

Correct!

*Note there are several ways to solve for these types of problems. I used substitution*

You might be interested in
A ball is hit vertically upwards from a cliff, which is 80 m above the sea. The displacement
Stels [109]

Answer:

a) 8 seconds

b) 3 seconds

c) 170 meters

Step-by-step explanation:

a) When the ball lands in the sea, s = -80.

-80 = 30t − 5t²

5t² − 30t − 80 = 0

t² − 6t − 16 = 0

(t + 2) (t − 8) = 0

t = -2 or 8

t = 8 seconds

b) The ball reaches its highest point when the velocity is 0 (or at the vertex of the parabola).

t = -b / (2a)

t = -30 / (2 × -5)

t = 3 seconds

c) The highest point is:

s = 30(3) − 5(3)²

s = 45

So the ball rises 45 meters, falls 45 meters, then falls 80 meters.

The total distance traveled is 45 + 45 + 80 = 170 meters.

6 0
2 years ago
How can you tell when an equation in one variable has infinitely many solutions or no solution?
Masteriza [31]

Answer:

A system has infinitely many solutions when it is consistent and the number of variables is more than the number of nonzero rows in the rref of the matrix. For example if the rref is ��has solution set (4-3z, 5+2z, z) where z can be any real number.

6 0
3 years ago
One Endpoint is 9,18 and the midpoint is 14,16 what the other end point
Valentin [98]
\bf \textit{middle point of 2 points }\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
%  (a,b)
&({{ 9}}\quad ,&{{ 18}})\quad 
%  (c,d)
&({{ x}}\quad ,&{{ y}})
\end{array}\qquad
%   coordinates of midpoint 
\left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right)

\bf \left( \cfrac{x+9}{2}~,~\cfrac{y+18}{2} \right)=\stackrel{\textit{midpoint}}{(14,16)}\implies 
\begin{cases}
\cfrac{x+9}{2}=14\\\\
x+9=28\\
\boxed{x=19}\\
-------\\
\cfrac{y+18}{2}=16\\\\
y+18=32\\
\boxed{y=14}
\end{cases}
7 0
3 years ago
The price p (in dollars) and the demand X for a particular clock radio are related by the equation X = 3000 -10p. Find and answe
alukav5142 [94]

The price p based on the equation given is p = 3000 - 0.1x.

<h3>How to express the price?</h3>

The equation given in the question is x = 3000 - 10p. The price(p) will be:

x = 3000 - 10p.

Make p the subject of the formula

x + 10p = 3000

10p = 3000 - x

p = (3000 - x)/10

p = 3000 - 0.1x

The revenue will be price multiplied by quantity. This will be:

= (3000 - 0.1x) × x

= 3000x - 0.1x²

The marginal revenue will be calculated after differentiating. This will be:

= 3000x - 0.1x²

= 3000 - 0.2x

The demand which is the quantity based on the information will be:

3000 - 0.2x = 0

0.2x = 3000

x = 1500

Learn more about demand on:

brainly.com/question/1245771

#SPJ1

6 0
1 year ago
What is his average speed for end the entire trip 280 miles<br> ?
-BARSIC- [3]

Answer:

20mph

Step-by-step explanation:

because when you divide the 280 it goes by 20 mph to get to 280 miles by quarters but in 20s

7 0
2 years ago
Other questions:
  • The fastest a human has ever run is 27 miles per hour how many miles per minute did the human run
    9·1 answer
  • Select the converse of "If you saw the movie, then you know how it ends."
    7·2 answers
  • What is the simplified expression or 5(2 + 4) + (8 - 2) =​
    12·2 answers
  • Find x3 -y3,if x-y=5 and xy=14
    12·1 answer
  • The diagram shows a rectangle and a diagonal of the rectangle. Length=8.5cm. Width=5.6cm. Work out the length of the diagonal of
    13·1 answer
  • The cost of a cab ride is given by the function C= 1.80 + 1.5 d , where d is the number of miles traveled and C is in dollars. W
    10·1 answer
  • Round 8.547 to the nearest whole number
    5·2 answers
  • Write a system of two linear equations in two variables that represents this real life problem and Solve the system of linear eq
    6·1 answer
  • An unknown polynomial is added to the expression -3x^3+2x-5 and the resulting sum is 4x^3+7x^2-3. what is the unknown polynomial
    8·1 answer
  • Choose whether the expression is a result of multiplying
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!