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
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answers
Answer:
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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.
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Answers
Answer:
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Step-by-step explanation:
because on a table, -21 and 21 are lined up together.
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answers
Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
Answer:
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Step-by-step explanation:
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Answers
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3 times Marie's age is equal to 50, so you divide 50 by 3.
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Answers
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Answers
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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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
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Answers
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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:
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Answer:
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Step-by-step explanation:
2 pts
Question 4
Find the value of each expression. Round decimals to the nearest hundredth if
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Answers
Answer:
67 and -1
Step-by-step explanation:
You always multiply first so its 7+64-4 and that becomes 67
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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.