Objective: Solve systems of equations with three variables using addition/elimination.
Solving systems of equations with 3 variables is very similar to how we solve systems with two variables. When we had two variables we reduced the system down
to one with only one variable (by substitution or addition). With three variables
we will reduce the system down to one with two variables (usually by addition),
which we can then solve by either addition or substitution.
To reduce from three variables down to two it is very important to keep the work
organized. We will use addition with two equations to eliminate one variable.
This new equation we will call (A). Then we will use a different pair of equations
and use addition to eliminate the same variable. This second new equation we
will call (B). Once we have done this we will have two equations (A) and (B)
with the same two variables that we can solve using either method. This is shown
in the following examples.
Example 1.
3x +2y − z = − 1
− 2x − 2y +3z = 5 We will eliminate y using two different pairs of equations
5x +2y − z = 3
1
3x +2y − z = − 1 Using the first two equations,
− 2x − 2y +3z = 5 Add the first two equations
(A) x +2z = 4 This is equation (A), our first equation
− 2x − 2y +3z = 5 Using the second two equations
5x +2y − z = 3 Add the second two equations
(B) 3x +2z = 8 This is equation (B), our second equation
(A) x +2z = 4 Using (A) and (B) we will solve this system.
(B) 3x +2z = 8 We will solve by addition
− 1(x +2z) =(4)( − 1) Multiply (A) by − 1
− x − 2z = − 4
− x − 2z = − 4 Add to the second equation, unchanged
3x +2z = 8
2x = 4 Solve, divide by 2
2 2
x = 2 We now have x! Plug this into either(A) or(B)
(2) +2z = 4 We plug it into (A),solve this equation,subtract 2
− 2 − 2
2z = 2 Divide by 2
2 2
z = 1 We now have z! Plug this and x into any original equation
3(2) +2y − (1)= − 1 We use the first, multiply 3(2) =6 and combine with − 1
2y + 5= − 1 Solve,subtract 5
− 5 − 5
2y = − 6 Divide by 2
2 2
y = − 3 We now have y!
(2, − 3, 1) Our Solution
As we are solving for x, y, and z we will have an ordered triplet (x, y, z)
ANSWER PLSSS!!!!!!
What is Ann's speed at 7 mins? give a reason to support your answer
Answer:
40 Miles per hour
Step-by-step explanation:
The answer is in the graph.
Which of the two elements below have similar properties?
Chlorine (CI) and Zinc (Zn)
Sodium (Na) and Fluorine (F)
Potassium (K) and Francium (Fr)
Magnesium (Mg) and Helium (He)
Answer:
C
Step-by-step explanation:
1. Does the table below show a proportional relationship? If so, what is the value of y when
x is 20? If not, explain why not. (2 points)
12
3
14
11
16
19
18
27
Which fraction represents the solution to -6/5/(-3/25) in simplest form?
A. -10
B. -18/125
C. 10
D. 18/125
The fraction represents the solution to (-6/5)/(-3/25) in the simplest form will be 10. Then the correct option is C.
What is Algebra?Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.
The fraction numbers are given below.
-6/5 and -3/25
Then the division of the numbers -6/5 and -3/25 will be given by putting a division sign between them. Then we have
⇒ (-6/5) ÷ (-3/25)
⇒ (-6/5) / (-3/25)
⇒ (6/5) x (25 / 3)
⇒ 150 / 15
⇒ 10
The part that addresses the answer for (- 6/5)/(- 3/25) in the most straightforward structure will be 10. Then the right choice is C.
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ2
How would i know if a line on a graph has passed the vertical line test?
Answer:
The vertical line will only pass the graph line once.
Step-by-step explanation:
For example, I found an example online. The vertical line intersects a circle twice. But on a horizontal squiggly line, it only touches it once. So the circle is NOT a function but the squiggly line IS a function.
Hope this helps!! Brainiest is appreciated!! Happy Holidays!!!!
Solve for the unknown variable and verify your answer. 2.8(3d – 2) = –12.32 *
Answer?
Answer:
-.8
Step-by-step explanation:
divide both sides by 2.8
3d-2=-4.4
add two to both sides
3d=-2.4
divide both sides by 3
d=-.8
Snare Drum
Backbeats
Bass Guitar
Notes
3
2
90
60
120
80
Part A. Are the two quantities proportional? Justify your answer.
Yes they because they have the same constant proportionality.
Part B. What is the constant of proportionality? *
0.77
Answer : what do i answer
Step-by-step explanation:
Which equation is equivalent to 9x+4y=16
y=9/4x+4
y=-9/4x+4
y=4/9x+16/9
y=-4/9x+4/7
Answer:
The answer is 4/9x+16/9
Step-by-step explanation:
Which is the graph of the function f(x) = x^3 -3x^2-4x
Answer:
b
Step-by-step explanation:
I need answer ASAP OLZ
Answer:
the second one
Step-by-step explanation:
My friend Dubble got 10 rews and corazs for about $32. Rews for $2 each and some corazs for $8 each
Answer:
"Dubble" bought 10 rews for $2.00 each and 1 corazs for $8.00 each
-I put quotation marks on Dubble bc i didnt know if it was a boy or girl name sorryyy its.. um.. unique :) -
Step-by-step explanation:
The price for the rews is 10x 2 because the price of each is $2 and he got 10 so he spent $20 on rews.
Then you subtract the total amount of money "Dubble" used buying these things and the amount of money "Dubble" used on the rews which is 32-20=8
The last step is that you divide 8 by the pice of each corazs which is 8 divided by 8 so the answer is 1.
Hope this helped you sorry im a little late bubs.<3
kyle has $1.60 in change in his pocket. He has the same number of quarters as nickels. He has 4 more dimes than quarters. How many of each coin does he have?
cotA . cos(30°-A) - sin ( 30°- A) = ✓3÷2
Answer:
cotA. cos(30° - A) - sin(30° - A) = √3/2
⇔
Step-by-step explanation:
What's the average between 63 and 162
Answer:
112.5
Step-by-step explanation:
The average is calculated as
average = [tex]\frac{sum}{count}[/tex], then
average = [tex]\frac{63+162}{2}[/tex] = [tex]\frac{225}{2}[/tex] = 112.5
How many solutions does the following equation have?
3x + 7 + 2x = 5x + 7
One. Many. None
Answer:
Infinite/many
Step-by-step explanation:
3x + 7 + 2x = 5x + 7
3x + 2x + 7 = 5x + 7
5x + 7 = 5x + 7
5x - 5x + 7 = 7
7 = 7
Infinite solutions
Answer: many (all real numbers)
Step-by-step explanation:
1) add 2x and 3x to give you 5x
You now have 5x+7=5x+7
2) you can simplify this by subtracting 7 on both sides and dividing by 5
3) you are then left with x=x
Find the product. Write your answer as a fraction in simplest form.
-3/10 × (-8/15)=??
Answer: simplify the expression
4/15
Answer:
8/15 is already in the simplest form
Step-by-step explanation:
PLEEEASE HELP ME ASAP!!!!!!! thank you so so much!!! *will ofc give brainliest*
===============================================
Work Shown:
[tex]V = \frac{4}{3}\pi*r^3\\\\V = \frac{4}{3}\pi*(2t)^3\\\\\frac{4000\pi}{3} = \frac{4}{3}\pi*(2t)^3\\\\4000\pi = 4\pi*(2t)^3\\\\1000 = (2t)^3\\\\(2t)^3 = 1000\\\\(2t)^3 = 10^3\\\\2t = 10\\\\t = 5\\\\[/tex]
-----------------
Notes:
In line 2, I replaced r with 2t because the radius r is increasing at a rate of 2 cm per second. So if t is the number of seconds, then 2t is the radius in cm at time t.In line 4, I multiplied both sides by 3 to clear out the fractions. On the next line, I divided both sides by 4pi.1+2+3+...98+99+100 what's the total and how many pairs will there be?
Answer:
5050 and 100 pairs
Step-by-step explanation:
Given FGH with vertices F(-1, 3), G(-5, 1), and H(-3, 5) reflected by Rx-axis
Find the coordinate of vertices F'G'H the image of FGH
1, F(-1, 3), G(-5, 1), and H(-3, 5)
2, F(-1, -3), G(-5, -1), and H(-3, -5)
3, F(1, 3), G(5, 1), and H(3, 5)
4, F(-1, 3), G(-5, 1), and H(-3, -5)
Answer:
Option F is true.
Step-by-step explanation:
The rule of reflection across the x-axis
P(x, y) → P'(x, -y)
For example, when a point P with coordinates (1, 2) is reflected across the x-axis, the coordinates of the image of point P will be: P'(1,-2).
i.e.
P(x, y) → P'(x, -y)
P(1, 2) → P'(1, -2)
Now, given FGH with vertices F(-1, 3), G(-5, 1), and H(-3, 5) reflected by Rx-axis.
Using the rule of reflection across the x-axis
P(x, y) → P'(x, -y)Thus, the coordinate of vertices F'G'H the image of FGH will be:
F(-1, 3) → F'(-1, -3)
G(-5, 1) → G'(-5, -1)
H(-3, 5) → H'(-3, -5)
Hence, option F is true.
Explain, in terms of the structure of the expression for L(t) , why Lincoln's balance can never be 499.
Answer:
after 19 years, Helen's balance is still larger than Lincoln's but after 20 years, Lincoln's balance will be larger than Helen's.
Step-by-step explanation:
My question is in the picture
1. Geneva has 24 points. Then her spin lands on blue. What is her score now? Explain.
Blue = + 4. This means that you will need to add 4 to 24, causing Geneva's new amount of points to be 28. You could put down,
Geneva now has 28 points. Blue is equal to +4, so I added 24 + 4 to get 28.
2. Geneva and Juan start a new game. Each player has 0 points.
a. Geneva's first two spins are yellow and red. What is her score now? Explain.
Geneva's score is now -2. Yellow is equal to -4, red is equal to +2. -4 + 2 = -2.
b. Juan's first two spins are red and green. What is his score now? Explain.
Red is equal to +2 and green is equal to -1. That means that Juan has 1 point because 2 + -1 = 1.
c. Which player has a greater score now? Explain.
Juan has a greater score. He has a greater score because 1 is greater than -2.
Write an equation in slope-intercepts form for the line that passes through (5, -4) and is perpendicular to the line described by 2x-10y=0
EXPLAIN what you did in each step to arrive at your answer plz
Answer:
y = -5x + 21
Step-by-step explanation:
First, put 2x - 10y = 0 into slope intercept form to find the slope:
Subtract 2x from both sides:
-10y = -2x
Divide each side by -10:
-10y = -2x
y = 1/5x
So, the slope of the line is 1/5.
Perpendicular lines have opposite reciprocal slopes, so the slope of the other line will be -5.
Then, use the equation y = mx + b to plug in the slope and the point given.
Solve for b:
y = mx + b
-4 = -5(5) + b
-4 = -25 + b
21 = b
Lastly, plug in the slope and b into y = mx + b to create the equation in slope intercept form:
y = -5x + 21 is the equation
Zoologists have been carefully observing an
endangered species in the foothills. They have
noticed that the population, P, of the animal in the
foothills has increased by 3% each year. Their
observations indicated that 500 of the animals
were initially in their study.
Which rule can be used to estimate the
population of the endangered animal over time?
Answer:
i would do last option
Step-by-step explanation:
Which arrangement shows 275, 5.36, 535, and 336 in order from least to greatest?
275, 5.36, 336, 535
535, 5.36, 275,336
5.36, 275,336, 535
5.36, 275, 535, 336
Answer:
I have a feeling it's 5.36, 275, 336, 535.
Sorry if I'm wrong.
Step-by-step explanation:
Answer:
C is the answer........
Please help me I can't figure this out.
Answer:
C. 256 square inches
Step-by-step explanation:
if each side of the cube is 8, and the height is 4 your equation would be 8x8x4=256
What is the square root of 5900?
Answer:
76.81
Step-by-step explanation:
bshsbdjsbzjdnskzbsjzbjs sjs
please help i cant figure this out
Tyson has a collection of 60 sports ribbons. Of these ribbons, 30% are first place ribbons, 45% are second place ribbons, and the rest are third place ribbons. How many third place ribbons are in Tyson’s sports ribbon collection?
answers:
27
32
15
18
Answer:
15
Step-by-step explanation:
First do, 30% + 45% = 75%. Then do, 100-75=25.
Lastly,
proportions:
x/60 = 25/100
So your answer is, 15.
A truck and a car go at the same time against each other from two cities, which are at a distance of 400 km from each other. If the vehicles are moving at a constant speed of 68 km / h and 82 km / h, respectively, find after how long they have met?
Answer: after about 96 Minutes
Step-by-step explanation:
write 1.054 in words
Answer:
one and fifty-four thousandths
Step-by-step explanation:
The 1 is easy.
The 4 is in the thousandths place, so the decimal part is 54/1000.
Answer: one and fifty-four thousandths
(x - 2)^5 binomial expansion