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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:

1/2

Step-by-step explanation:

Given that,

[tex]\lim_{n \to 1} (\dfrac{1+\cos\pi x}{\tan^2\pi x})[/tex]

Using L Hospital's rule to find it :

[tex]\lim_{n \to a} \dfrac{f(x)}{g(x)}= \lim_{n \to a} \dfrac{f'(x)}{g'(x)}[/tex]

We have,

a = 1, [tex]f(x)=1+\cos\pi x, \ \ g(x)=\tan^2\pi x[/tex]

[tex]f'(x)=\dfrac{d}{dx}(1+\cos\pi x)\\\\=-\pi \sin \pi x\ .....(1)[/tex]

[tex]g'(x)=\dfrac{d}{dx}(\tan^2\pi x)\\\\=2\tan\pi x\times \sec^2\pi x\times \pi\ .....(2)[/tex]

From equation (1) and (2) :

[tex]\lim_{n \to 1} \dfrac{f(x)}{g(x)}= \lim_{n \to 1} \dfrac{-\pi \sin\pi x}{2\tan \pi x\times \sec^2\pi x \times \pi}\\\\\lim_{n \to 1} \dfrac{-\pi \sin\pi x}{2\tan \pi x\times \sec^2\pi x \times \pi}\\\\=\lim_{n \to 1} \dfrac{-1}{2}\times\cos^3\pi x\\\\=\dfrac{-1}{2}\times \cos^3\pi \\\\=\dfrac{1}{2}[/tex]

So, the value of the given function is 1/2.

Answer:

Results are below.

Step-by-step explanation:

Giving the following information:

Principal= $450

Number of periods= 8 years

Interest rate= 6%

We will determine the interest earned and future value using simple interest and compound interest:

Simple interest:

I= P*r*t

I= 450*0.06*8= $216

Total Future Value= I + P

Total Future Value= 216 + 450= $666

Compound interest:

I= [P*(1+r)^t] - P

I= [450*(1.06^8)] - 450= $267.23

Total Future Value= P*(1+r)^t

Total Future Value= 450*1.06^8

Total Future Value= $717.23

Answer:

Step-by-step explanation:

6

Answer: y=1

Step-by-step explanation:

Answer:

$246.75

Step-by-step explanation:

11.75 x 21 = 246.75

hope this helps <3

Answer:

If the student worked 21 hours this month, she will earn $246.75.

Step-by-step explanation:

Let [tex]x[/tex] equal hours.

If the student earns $11.75 per hour, we can represent this with the expression:

[tex]11.75x[/tex]

If she worked 21 hours this month, then:

[tex]x=21[/tex]

With that information, we can substitute [tex]21[/tex] for [tex]x[/tex] in the initial expression:

[tex]11.75(21)[/tex]

Multiply:

[tex]246.75[/tex]

Therefore, if the student worked 21 hours this month, she will earn $246.75.

-

We can check our work by setting the initial expression equal to our solution:

[tex]11.75x=246.75[/tex]

Divide both sides of the equation by the coefficient of [tex]x[/tex], which is [tex]11.75[/tex]:

[tex]x=21[/tex]

Since this quotient matches the number of hours she worked, our solution is correct!

Answer: A. Not a function. B. Is a function. C. Not a function. D. Not a function.

Step-by-step explanation:

Step-by-step explanation:

78 divided by 4 = 19.5 pounds of bird food each.

Answer:

19.5 pounds per bird feeder

Step-by-step explanation:

78/4

Answer:

22.75

I did some work to try and find this answer sorry if it is wrong I tried.

Answer:

y= -1/3x + 4

Step-by-step explanation:

m in this case is (-1/3)

and b is (4)

knowing that you can just plug them into the equation (y=mx+b)

1.When all the three cut outs of the angles A, B, C placed adjacent to each other at a point, then it forms a line forming a straight angle, i.e. 180°.

Flence, it is proved that the sum of the three angles of a triangle is 180°.

Therefore, ∠A + ∠B + ∠C =180

Mark them brainliest

Answer:

Y goes like this: -3, -2, -1, 0, 1

Step-by-step explanation:

All you have to do is replace the X in the equation with the X in the chart.

For example, to find the first Y I just did:

y= -2-1

And whatever the thing equals is Y

Answer:

n+35=180

n=180-35

n=145

Answer:

Hi there! The answer is $1.86. Hope this helps! c:

Step-by-step explanation:

First, convert 15% to a decimal.

15% / 100 = 0.15

Then, multiply.

0.15 * 12.40 = $1.86

Since 15% of 12.40 is $1.86, then Jamie left a $1.86 tip.

Answer: y=7x^2−42x+69

Step-by-step explanation:

Answer:

Step-by-step explanation:

Table representing the function 'f' is,

x     -3      2       3        7    

y     -2      8      10       18

In this table for every input value of x, there is a different output value.

So the function is one to one function.

Therefore, inverse of the given function will have the table as,

x       -2      8      10       18

y       -3      2       3        7    

Answer:

y - 2= -5(x + 3)... (the red one) is the correct answer!!!

HOPE THIS HELPED!!!

Answer:

Dividing two negative values results in a positive value. Reorder −4 - 4 and 2x5 2 x 5 . Rewrite in slope-intercept form. Using the slope-intercept form, the slope is 25 .

Answer: C is the domain of the function

Step-by-step explanation:

y=f(x) and x in y=f(x) is domain.

Answer:

-2

Step-by-step explanation:

By using an equation, we may state that the number is = -2.

Let's use the quantity "X" as the variable in our inquiry. The number is - since 21 is less than 11 times "X," which results in seven times a number that has been decreased by 29.

Hence we can say that after forming the equation according to the question the answer is, X=-2.

Know more about Equations click here:

https://brainly.com/question/2228446

#SPJ2

Answer:

you will need 4 cups of brown rice because it says per cup of brown rice

Step-by-step explanation:

ok so,

5 cups of chicken broth= 1 cup of brown rice

so if there's 20 cups of chicken broth, then:

20/5(since 5 equals 1 cup of brown rice)

=4 cups of brown rice

Answer:

21

Step-by-step explanation:

Let x be the amount of ticket for each game

Given

The expression 8x + 62 represents the total cost of the football game

The total coat for the.game will be

8(7)+62

= 56+62

= 118

If 9x + 34 represents the total cost of the baseball game. The total coat will be;

9(7)+34

= 63+34

=97

To know how much more football game costs, we will take the difference in their cost.

Difference = 118-97

Difference= 21

Hence football game costs 21 more than baseball

Answer:

If we want to cover the base of the prism having dimensions 2 cm × 1 cm with cm length of cube, then there will be (4 × 2) = 8 cubes that can occupy the base.

Step-by-step explanation:

Answer:

cost of crab meals = $20

cost of vegetarian meals = $38

Step-by-step explanation:

Let

x = cost of crab meals

y = cost of vegetarian meals

Troop A

12 crab meals and 23 vegetarian meals, with total receipts of $916.

12x + 23y = 916

Troop B

12 crab meals and 12 vegetarian meals, bringing in a total of $696

12x + 12y = 696

12x + 23y = 916 (1)

12x + 12y = 696 (2)

Subtract (2) from (1)

23y - 12y = 916 - 696

11y = 220

y = 220/11

= 20

y = 20

Substitute y = 20 into (1)

12x + 23y = 916

12x + 23(20) = 916

12x + 460 = 916

12x = 916 - 460

12x = 456

x = 456/12

= 38

x = 38

cost of crab meals = $20

cost of vegetarian meals = $38

Answer:

The answer for the question is C

Answer:

The answer is D.) the exponent that you raise to a base in order to get a number.

Step-by-step explanation:

I got it on usatestprep.

Answer:

The answer is D

Step-by-step explanation:

Answer:

Exactly one pair of opposite sides are parallel

Step-by-step explanation:

A trapezoid is a plane shape quadrilateral that has exactly one pair of its sides parallel.

The parallel sides must occur for it to be a trapezoid. If they do not, it is most likely another shape. They could occur between the top and bottom sides while the left and right sides remain non-parallel, or vice-versa.

The other options given do not fall into the description of a trapezoid, as its opposite sides and diagonals are not always congruent.

9514 1404 393

Answer:

Step-by-step explanation:

The graph of an inverse relation is the reflection of the graph of the relation over the line y = x. That interchanges the coordinates of the points of the function. (-2, 4) becomes (4, -2) when so reflected, for example.