Ask question

Ask question

All categories

3 years ago

15

Solve the system by elimination.(show your work)

2 answers:

PilotLPTM [1.2K]3 years ago

6 0

Answer:

x = 1 , y = 1 , z = 0

Step-by-step explanation by elimination:

Solve the following system:

{-2 x + 2 y + 3 z = 0 | (equation 1)

-2 x - y + z = -3 | (equation 2)

2 x + 3 y + 3 z = 5 | (equation 3)

Subtract equation 1 from equation 2:

{-(2 x) + 2 y + 3 z = 0 | (equation 1)

0 x - 3 y - 2 z = -3 | (equation 2)

2 x + 3 y + 3 z = 5 | (equation 3)

Multiply equation 2 by -1:

{-(2 x) + 2 y + 3 z = 0 | (equation 1)

0 x+3 y + 2 z = 3 | (equation 2)

2 x + 3 y + 3 z = 5 | (equation 3)

Add equation 1 to equation 3:

{-(2 x) + 2 y + 3 z = 0 | (equation 1)

0 x+3 y + 2 z = 3 | (equation 2)

0 x+5 y + 6 z = 5 | (equation 3)

Swap equation 2 with equation 3:

{-(2 x) + 2 y + 3 z = 0 | (equation 1)

0 x+5 y + 6 z = 5 | (equation 2)

0 x+3 y + 2 z = 3 | (equation 3)

Subtract 3/5 × (equation 2) from equation 3:

{-(2 x) + 2 y + 3 z = 0 | (equation 1)

0 x+5 y + 6 z = 5 | (equation 2)

0 x+0 y - (8 z)/5 = 0 | (equation 3)

Multiply equation 3 by 5/8:

{-(2 x) + 2 y + 3 z = 0 | (equation 1)

0 x+5 y + 6 z = 5 | (equation 2)

0 x+0 y - z = 0 | (equation 3)

Multiply equation 3 by -1:

{-(2 x) + 2 y + 3 z = 0 | (equation 1)

0 x+5 y + 6 z = 5 | (equation 2)

0 x+0 y+z = 0 | (equation 3)

Subtract 6 × (equation 3) from equation 2:

{-(2 x) + 2 y + 3 z = 0 | (equation 1)

0 x+5 y+0 z = 5 | (equation 2)

0 x+0 y+z = 0 | (equation 3)

Divide equation 2 by 5:

{-(2 x) + 2 y + 3 z = 0 | (equation 1)

0 x+y+0 z = 1 | (equation 2)

0 x+0 y+z = 0 | (equation 3)

Subtract 2 × (equation 2) from equation 1:

{-(2 x) + 0 y+3 z = -2 | (equation 1)

0 x+y+0 z = 1 | (equation 2)

0 x+0 y+z = 0 | (equation 3)

Subtract 3 × (equation 3) from equation 1:

{-(2 x)+0 y+0 z = -2 | (equation 1)

0 x+y+0 z = 1 | (equation 2)

0 x+0 y+z = 0 | (equation 3)

Divide equation 1 by -2:

{x+0 y+0 z = 1 | (equation 1)

0 x+y+0 z = 1 | (equation 2)

0 x+0 y+z = 0 | (equation 3)

Collect results:

Answer: {x = 1 , y = 1 , z = 0

nata0808 [166]3 years ago

5 0

Answer:

x = 1 , y = 1 , z = 0

Step-by-step explanation:

Add first equation to third one

-2x + 2y + 3z = 0

+

2x + 3y + 3z = 5

----------------- -------

5y + 6z = 5 (4th equation)

Subtract second equation to first one

-2x + 2y + 3z = 0

-

-2x - y + z = -3

------------------ --------

3y + 2z = 3 (5th equation)

Multiply 5th equation by 3

3*(3y + 2z) = 3*3

9y + 6z = 9 (6th equation)

Subtract 6th equation to fourth one

5y + 6z = 5

-

9y + 6z = 9

-----------

-4y = -4

Solve for y

-4y = -4

y = (-4)/(-4)

y = 1

Replace this value in 4th equation and solve for z

5(1) + 6z = 5

6z = 5-5

6z = 0

z = 0

Replace y and z values obtained in first equation and solve for x

-2x + 2y + 3z = 0

-2x + 2(1) + 3(0) = 0

-2x + 2 = 0

-2x = -2

x = (-2)/(-2)

x = 1

You might be interested in

Factor 18x^2-3x+24x-4

zhannawk [14.2K]

3x(6x-1)+4(6x-1)

(3x+4)(6x-1) is the answer

5 0

3 years ago

SOMEONE HELP PLEASE HELP

kotegsom [21]

triangle XBR is similar to triangle YNJ.

Similar triangles are triangles with lengths in proportion, and congruent corresponding angles. When naming a similar triangle, the letters or vertexes are listed in a certain order. For instance, angle X is the same as angle Y so those two letters have to be in the same position. In this case, they are both the first letters. Angle B is congruent to angle N and angle R is congruent to angle J so they will also have to be in corresponding positions. The side lengths are extraneous information that can be used to check, but otherwise I would just stick with angles. Hope this helps!

6 0

4 years ago

32b=8<br> Whats the number for b??

kherson [118]

Answer:

the answer is 4

Step-by-step explanation:

32÷8=4 therefore b is 4

3 0

3 years ago

Read 2 more answers

It costs $38 for 2 people to go to the movie theater. 40% of the money was for snacks.What was the cost of each movie ticket?

stira [4]

Answer:

11.4

Step-by-step explanation:

40% of 38 is 15.2, 38-15.2=22.8. 22.8/2=11.4 (since there's two people)

4 0

4 years ago

3 cards are drawn from a standard deck without replacement. What is the probability that at least one of the cards drawn is a re

Rudik [331]

Answer: $\dfrac{15}{17}$

Step-by-step explanation:

Total number of cards in a deck = 52

Number of red cards = 26

Number of cards not red =

Number of ways to draw not red cards = $^{26}C_3$

Total ways to draw 3 cards = $^{52}C_3$

The probability that none of three cards are red = $\dfrac{^{26}C_3}{^{52}C_3}$

$=\dfrac{\dfrac{26!}{3!(26-3)!}}{\dfrac{52!}{3!(52-3)!}}$ [∵ $^nC_r=\dfrac{n!}{r!(n-r)!}$ ]

$=\dfrac{\dfrac{26\times25\times24\times23!}{(23)!}}{\dfrac{52\times51\times50\times49!}{3!(49)!}}=\dfrac{2}{17}$

Now , the probability that at least one of the cards drawn is a red card = 1- Probability that none cards are red

$=1-\dfrac{2}{17}=\dfrac{17-2}{17}=\dfrac{15}{17}$

Hence, the required probability = $\dfrac{15}{17}$

6 0

3 years ago