please help me with this system of equations problem before I go insane the preferable solving methods would be through substitution or elimination
Answers
Answer:
x=8, y=0, z=-3
Step-by-step explanation:
Preferable is substitution because there is less room for mistakes but its long so here goes bare with me on this one :D
Name your equations
4x+2y-5z=47 (first eq)
x-2y+6z=-10 (second eq)
9x-7y-z=75 (third eq)
Lets take the easiest eq to isolate one variable lets take 2nd eq
[tex]x-2y+6z=-10\\x=2y-6z-10[/tex]
now this becomes our fourth eq
now again take the easiest eq to isolate another variable lets take the 3rd eq
[tex]9x-7y-z=75\\9x-7y-75=z[/tex]
now this becomes our fifth eq
and now plug in our fifth eq in the fourth eq because we now have z in terms of x and y
[tex]x=2y-6z-10\\x=2y-6(9x-7y-75)-10\\x=2y-54x+42y+450-10\\x+54x=2y+42y+450-10\\55x=44y+440\\\\x=\frac{44y+440}{55}[/tex]
and now we got our sixth equation which is x only in terms of y.
now we plug in our sixth equation in our fifth eq to get z in terms of y only
[tex]z=9x-7y-75\\\\z=9(\frac{44y+440}{55}) -7y-75\\z=\frac{396y+3960}{55} -7y-75\\z=\frac{396y+3960-385y-4125}{55} \\z=\frac{11y-165}{55}[/tex]
now we have our seventh eq and x &z in terms of just one variable y , now we put equation of z and x which is our sixth eq and seventh eq in our first eq.
[tex]4x+2y-5z=47\\\\4(\frac{44y+440}{55})+2y-5(\frac{11y-165}{55}) =47\\\\\frac{176y+1760}{55} +2y-47=\frac{11y-165}{11} \\\\\frac{176y+1760}{55} -\frac{11y-165}{11} -47=-2y\\\\\frac{176y+1760}{55}-(y-15) -47=-2y\\\\\frac{176y+1760}{55} -y-32=-2y\\\\\\frac{176y+1760}{55}=-2y+y+32 \\\\176y+1760=55(-y+32)\\176y+1760=-55y+1760\\176y-55y=1760-1760\\121y=0\\y=0[/tex]
and now finally we got y=0 now we need the value of x and z, put the value of y=0 in our seventh eq (z equation)
[tex]z=\frac{11y-165}{55} \\\\z=\frac{11(0)-165}{55} \\\\z=\frac{-165}{55}\\\\z=-3[/tex]
and now we put the value of y=0 in our sixth eq (x equation)
[tex]x=\frac{44y+440}{55} \\\\x=\frac{44(0)+440}{55} \\\\x=\frac{440}{55} \\\\x=8[/tex]
and now we got all the three values and hence the solution of the system of equation is
x=8, y=0, z=-3
Related Questions
helpppp quickkkkkkkkk
Answers
Answer:
your answer is the last on the bottom
Please Help, this is 20pts worth it.. Please Don’t waste my points.. please help..
Answers
Answer:
1. 7+62+5+4
2. 18+62+5
3.15+4+1
4.5 families
6. three
Step-by-step explanation:
Tickets to a 3D movie cost $12.50 for adults and $8.50 for children. The theater can seat up to 180 people. A total of $1826 was collected in ticket sales for the sold out 7:15 PM show. Determine the number of adult tickets and the number of children's tickets that were sold.
Answers
Let, number of children are x and number of adult are y.
Total number of seats, T = 180.
x + y = 180 ....1)
Tickets to a 3D movie cost $12.50 for adults and $8.50 for children.
So, total amount :
8.5x + 12.5y = A
8.5x + 12.5y = 1826 ....2)
Solving equation 1) and 2) , we get :
8.5x + 12.5( 180 - x ) = 1826
8.5x - 12.5x + 2250 = 1826
-4x = -424
x = 106
y = 180 - 106 = 74
Therefore, the number of adult tickets and the number of children's tickets that were sold are 74 and 106.
Hence, this is the required solution.
What is the value of n in the equation -1/2 (2n + 4) + 6 = -9 + 4(2n + 1)?
n =
Answers
Answer:
n=1
Step-by-step explanation:
Answer:
n=1
Step-by-step explanation:
1)which set of points is a function?
2)which order pears cause this relations not to be a function. why?
Answers
Answer:
First Question is B
Second Question is C
Step-by-step explanation:
You can’t have the same x values going to different y values
Lin has a scale model of a modern train. The model is created at a scale of 1 to 48. The height of the model train is 102 millimeters. What is the actual height of the train in meters? Round your answer to the thousandths (third) decimal place. Do not include units (meters) in your answer.
Answers
Carrie needs to determine the number of tiles that will fit in each row along the back of the shower. If the back of the shower measures 6 feet long and each tile is Two-thirds of a foot long, which equation shows how to determine the number of tiles that will fit in each row?
Answers
Answer: A6/ 2/3= 9
Step-by-step explanation:
We know that one tile is 2/3 ft long and we want to cover 6 ft (which is the given measure of the back of the shower).
To know the number of tiles needed, we will simply do cross multiplication as follows:
1 tile ...............> 2/3 ft
?? tiles ...........> 6 ft
Number of tiles = (6*1) / (2/3)
Number of tiles = 6 / (2/3)
Number of tiles = 9 tiles
Answer:
A). 6 ÷ 2/3 = 9
Step-by-step explanation:
Triangle ABC is dilated by a scale factor of 4. If A is located at (3,-5), where will A’ Be located?
Answers
Answer:
Step-by-step explanation:
Multiply both numbers by 4. That is your new coordinates. (12,-20)
what is the anwser to the question 35−10+35−10÷5
Answers
Answer:
its 10
Step-by-step explanation:
2 pts
Question 4
Find the value of each expression. Round decimals to the nearest hundredth if
necessary.
7+8x8-4
5-3(7-5)
Answers
Answer:
67 and -1
Step-by-step explanation:
You always multiply first so its 7+64-4 and that becomes 67
You have to distribute first so the problem would be 5-21+15 which is -1
3 times Marie’s age is equal to 50 plz show work
Answers
Answer:
m = 16 2/3
Step-by-step explanation:
Let m = maries age
3m = 50
Divide by 3
3m/3 = 50/3
m = 16 2/3
Answer:
Marie's age is 16.7 years
Step-by-step explanation:
3 times Marie's age is equal to 50, so you divide 50 by 3.
50 ÷ 3 = 16.6666666 repeating, round it to 16.7
Marie's age is 16.7 years.
Check: 3 x 16.7 = 50.1 so you round it to 50.
Hope this helps!
-Jerc
Which demonstrates the distributive property? *
a + b = b + a
O (a + b) + c = a + (b + c)
a(b + c) = ab + ac
a + 0 = a
Answers
Answer:
a(b + c) = ab + ac demonstrates the distributive property ⇒ C
Step-by-step explanation:
The distributive property is the product of a number by the sum of the other two numbers equal to the sum of the product of the number with each of the other two numbers.
Example: x(y + z) = xy + xz
Let us check the choices to find which of them demonstrates the distributive property
∵ a + b = b + a
→ Adding a and b equals to adding b and a,
∴ It demonstrates the commutative property
∵ (a + b) + c = a + (b + c)
→ Adding the sum of a and b to c equals to adding c to the sum of a and b
∴ It demonstrates the associative property
∵ a(b + c) = ab + ac
→ Multiplying a by the sum of b and c equals the sum of the products
of a, b and a, c
∴ It demonstrates the distributive property
∵ a + 0 = a
→ The additive identity is zero
∴ It demonstrates the additive identity property
∴ a(b + c) = ab + ac demonstrates the distributive property
(3) An estate was to be divided among five people. The first person received 1/8 of the estate. The next two people each received 1/5 of the estate. The fourth person received 1/10 of the estate. What fractional part of the estate did the last person receive?
Answers
Answer:
3/8
Step-by-step explanation:
An estate has to be divided among the 5 persons.
Given that the 1st person received 1/8 of the estate,
the 2nd person received 1/5 of the estate,
the 3rd person received 1/5 of the estate,
and the 4th person received 1/10 of the estate.
Let the 5th person received the x part of the estate.
The sum of all the fractional parts of one estate equals to 1, so
[tex]\frac 1 8+\frac 1 5+\frac 1 5+\frac 1 {10}+x=1[/tex]
[tex]\Rightarrow \frac 5 8 +x =1[/tex]
[tex]\Rightarrow x =1-\frac 5 8 =\frac 3 8.[/tex]
Hence, the last person received 3/8 of the estate.
i know it’s a lot to ask for but what are the answers for all of these you get 100 points and you get marked brainliest
Answers
What is the opposite of negative 21 or -21 ?
Answers
Answer:
21
Step-by-step explanation:
because on a table, -21 and 21 are lined up together.
2-10n plez helppppppppppppppppppppp
Answers
Answer:
2-10n=.............what. We can't figure out n given 2-10n without a solution
Step-by-step explanation:
What is the missing term in the factorization? 1872 -- 32 2(3x+?) (3x – 4) Enter your answer in the box.
Answers
Answer:
4
Step-by-step explanation:
..........................
what makes -1.3 a non integer
Answers
Answer:
Decimal and fractions numbers are non-integers
Step-by-step explanation:
The answer is the third choice because integers are whole numbers that can be positive, negative, or zero. -1.3, however, is not a whole number, so it is not an integer. The reason is the third choice as decimals and fractions are not integers. Hope it helps!
Sergio bought a new dryer for $337. How much did the dryer cost, rounded to the nearest hundred? NEED HELP PLEASE WILL GIVE BRAINEST
Answers
Answer:
300
Step-by-step explanation:
i just know
Answer:
337 rounded to the nearest hundred is 300.
Look at the tens place, it's less than 5 meaning everything after and itself is turned to a 0.
Step-by-step explanation:
Hope this explains it! <3
what a number named as a googolplexian might be ?
Answers
Answer:
A 1 with a hundred 0's following it
Step-by-step explanation:
1 1/4 divided by 2
a ) 2/3
b ) 5/8
c ) 1 1/3
d ) 2 1/12
Answers
Answer:
B) 5/8
Step-by-step explanation:
1.25/2
0.625
5/8
what your expect to gen.math subject
Answers
A line passes through the point (8, -7) and has a slope of -3/4
Write an equation in slope-intercept form for this line
Answers
Answer:
y = -3/4x -7
Step-by-step explanation:
hope this helps!
PLEASE HELP ME, IVE BEEN IGNORED FOR THE PAST 30 MINUTES AND THE ONLY PEOPLE WHO DO ANSWER ARE FAKE PEOPLE WITH WRONG ANSWERS. (IMAGE IN THE QUESTION)
Given the data in the table, complete the sentence.
Using a line of best fit for this data to predict the value of y when x = 10 is an example of
A. Interpolation
B. Extrapolation
C. Correlation
D. Causation
Answers
Answer:
isnt that extrapolation?
Step-by-step explanation:
A container of coffee is 1/6 full. The container contains 2/3 a pound of coffee. a. Write a division expression that represents the capacity of the container. b.Write a multiplication expression that represents the capacity of the container. c.Find the capacity of the container.
Answers
Answer:
(a) [tex]x= \frac 2 3\div \frac 1 6[/tex]
(b) [tex]x= \frac 2 3\times \frac 6 1[/tex]
(c) 4 pounds
Step-by-step explanation:
Let the capacity of the container is [tex]x[/tex].
The container has coffee which is 1/6 of the capacity of the container and the amount of coffee is 2/3 pounds.
So, 1/6 of the capacity of the container has 2/3 pound of coffee, i.e
[tex]\frac 1 6 \times x = \frac 2 3\cdots(i)[/tex]
(a) From the equation (i), the required division expression for the capacity of the box, x, is
[tex]x= \frac 2 3\div \frac 1 6[/tex]
(b) The division expression can be changed to multiplication expression by interchanging the numerator and the denominator of the divisor. So, from part (a), the required multiplication expression for the capacity of the box, x, is
[tex]x= \frac 2 3\times \frac 6 1\cdots(ii)[/tex]
(c) From equation (ii), the capacity of the box is
[tex]x= \frac 2 3\times 6= 4[/tex] pounds.
can someone help me on this question pretty please
Answers
Answer:
50 dollars an hour
Step-by-step explanation:
Simplify the expression. (6x+1/2)+(3x-3 1/2)
Answers
Answer:
Have a Spoopy Halloween lol its 9x-3
Step-by-step explanation:
(6x+1/2)+(3x-3 1/2)
= 6x+3x-3 1/2+1/2
= 9x-3
Answer:
[tex]9x - \frac{6}{2} [/tex]
Step-by-step explanation:
[tex](6x+1/2)+(3x-3 \: 1/2) \to \\ ( 6x + \frac{1}{2} ) +( 3x - 3 \frac{1}{2} ) \to \\ 9x + \frac{1}{2} - \frac{7}{2} \to \\ 9x - \frac{6}{2} [/tex]
♨Rage♨
Click on this message to get the question
Answers
Answer:
the picture is not clear
Step-by-step explanation:
could u retake the picture
Help me please this is a function questions need asap
Answers
Answer:
y hfaczdg eek Robocop teardrop outbound liquidz
Find the distance between the pair of points, round to the nearest tenth if necessary.
Answers
Step-by-step explanation:
distance between the two points is given by formula
d=
[tex] \sqrt{ {(x1 - x2)}^{2} + {(y1 - y2)}^{2} } = \sqrt{( - 2 - 4)^{2} + {( - 3 - 0)}^{2} } = \sqrt{( - 6)^{2} + ( - 3)^{2} } = \sqrt{36 + 9} = \sqrt{45} = \sqrt{9 \times 5} = 3 \sqrt{5} [/tex]