The elimination method for solving systems of linear equations uses the addition property of equality. You can add the same value to each side of an equation.
So if you have a system: x – 6 = −6 and x + y = 8, you can add x + y to the left side of the first equation and add 8 to the right side of the equation. And since x + y = 8, you are adding the same value to each side of the first equation.
If you add the two equations, x – y = −6 and x + y = 8 together, as noted above, watch what happens.
_{}
You have eliminated the y term, and this equation can be solved using the methods for solving equations with one variable.
Let’s see how this system is solved using the elimination method.
Example
 
Problem

Use elimination to solve the system.
x – y = −6
x + y = 8
 
_{}

Add the equations.
 
2x = 2
x = 1

Solve for x.
 
x + y = 8
1 + y = 8
y = 8 – 1
y = 7

Substitute x = 1 into one of the original equations and solve for y.
 
x – y = −6
1 – 7 = −6
−6 = −6
TRUE

x + y = 8
1 + 7 = 8
8 = 8
TRUE

Be sure to check your answer in both equations!
The answers check.
 
Answer

The solution is (1, 7).
 
Unfortunately not all systems work out this easily. How about a system like 2x + y = 12 and −3x + y = 2. If you add these two equations together, no variables are eliminated.
_{}
But you want to eliminate a variable. So let’s add the opposite of one of the equations to the other equation.
2x + y =12 → 2x + y = 12 → 2x + y = 12
−3x + y = 2 → − (−3x + y) = −(2) → 3x – y = −2
5x + 0y = 10
You have eliminated the y variable, and the problem can now be solved. See the example below.
Example
 
Problem

Use elimination to solve the system.
2x + y = 12
−3x + y = 2
 
2x + y = 12
−3x + y = 2

You can eliminate the yvariable if you add the opposite of one of the equations to the other equation.
 
2x + y = 12
3x – y = −2
5x = 10

Rewrite the second equation as its opposite.
Add.
 
x = 2

Solve for x.
 
2(2) + y = 12
4 + y = 12
y = 8

Substitute y = 2 into one of the original equations and solve for y.
 
2x + y = 12
2(2) + 8 = 12
4 + 8 = 12
12 = 12
TRUE

−3x + y = 2
−3(2) + 8 = 2
−6 + 8 = 2
2 = 2
TRUE

Be sure to check your answer in both equations!
The answers check.
 
Answer

The solution is (2, 8).
 
The following are two more examples showing how to solve linear systems of equations using elimination.
Example
 
Problem

Use elimination to solve the system.
−2x + 3y = −1
2x + 5y = 25
 

Notice the coefficients of each variable in each equation. If you add these two equations, the x term will be eliminated since
−2x + 2x = 0.
 

Add and solve for y.
 
2x + 5y = 25
2x + 5(3) = 25
2x + 15 = 25
2x = 10
x = 5

Substitute y = 3 into one of the original equations.
 
−2x + 3y = −1
−2(5) + 3(3) = −1
−10 + 9 = −1
−1 = −1
TRUE

2x + 5y = 25
2(5) + 5(3) = 25
10 + 15 = 25
25 = 25
TRUE

Check solutions.
The answers check.
 
Answer

The solution is (5, 3).
 
Example
 
Problem

Use elimination to solve for x and y.
4x + 2y = 14
5x + 2y = 16
 

Notice the coefficients of each variable in each equation. You will need to add the opposite of one of the equations to eliminate the variable y, as 2y + 2y = 4y, but
2y + (−2y) = 0.
 

Change one of the equations to its opposite, add and solve for x.
 
4x + 2y = 14
4(2) + 2y = 14
8 + 2y = 14
2y = 6
y = 3

Substitute x = 2 into one of the original equations and solve for y.
 
Answer

The solution is (2, 3).
 
Go ahead and check this last example—substitute (2, 3) into both equations. You get two true statements: 14 = 14 and 16 = 16!
Notice that you could have used the opposite of the first equation rather than the second equation and gotten the same result.
Many times adding the equations or adding the opposite of one of the equations will not result in eliminating a variable. Look at the system below.
3x + 4y = 52
5x + y = 30
If you add the equations above, or add the opposite of one of the equations, you will get an equation that still has two variables. So let’s now use the multiplication property of equality first. You can multiply both sides of one of the equations by a number that will result in the coefficient of one of the variables being the opposite of the same variable in the other equation.
This is where multiplication comes in handy. Notice that the first equation contains the term 4y, and the second equation contains the term y. If you multiply the second equation by −4, when you add both equations the y variables will add up to 0.
3x + 4y = 52 → 3x + 4y = 52 → 3x + 4y = 52
5x + y = 30 → −4(5x + y) = −4(30) → −20x – 4y = −120
−17x + 0y = −68
See the example below.
Example
 
Problem

Solve for x and y.
Equation A: 3x + 4y = 52
Equation B: 5x + y = 30
 

Look for terms that can be eliminated. The equations do not have any x or y terms with the same coefficients.
 

Multiply the second equation by −4 so they do have the same coefficient.
 

Rewrite the system, and add the equations.
 

Solve for x.
 
3x + 4y = 52
3(4) + 4y = 52
12 + 4y = 52
4y = 40
y = 10

Substitute x = 4 into one of the original equations to find y.
 
3x + 4y = 52
3(4) + 4(10) = 52
12 + 40 = 52
52 = 52
TRUE

5x + y = 30
5(4) + 10 = 30
20 + 10 = 30
30 = 30
TRUE

Check your answer.
The answers check.
 
Answer

The solution is (4, 10).
 
There are other ways to solve this system. Instead of multiplying one equation in order to eliminate a variable when the equations were added, you could have multiplied both equations by different numbers.
Let’s remove the variable x this time. Multiply Equation A by 5 and Equation B by −3.
Example
 
Problem

Solve for x and y.
3x + 4y = 52
5x + y = 30
 

Look for terms that can be eliminated. The equations do not have any x or y terms with the same coefficient.
 

In order to use the elimination method, you have to create variables that have the same coefficient—then you can eliminate them. Multiply the top equation by 5.
 

Now multiply the bottom equation by −3.
 

Next add the equations, and solve for y.
 
3x + 4y = 52
3x + 4(10) = 52
3x + 40 = 52
3x = 12
x = 4

Substitute y = 10 into one of the original equations to find x.
 
Answer

The solution is (4, 10).

You arrive at the same solution as before.
 
These equations were multiplied by 5 and −3 respectively, because that gave you terms that would add up to 0. Be sure to multiply all of the terms of the equation.
Felix needs to find x and y in the following system.
Equation A: 7y − 4x = 5
Equation B: 3y + 4x = 25
If he wants to use the elimination method to eliminate one of the variables, which is the most efficient way for him to do so?
A) Add Equation A and Equation B
B) Add 4x to both sides of Equation A
C) Multiply Equation A by 5
D) Multiply Equation B by −1

Just as with the substitution method, the elimination method will sometimes eliminate both variables, and you end up with either a true statement or a false statement. Recall that a false statement means that there is no solution.
Let’s look at an example.
Example
 
Problem

Solve for x and y.
x – y = 4
x + y = 2
 
x – y = 4
x + y = 2
0 = −2

Add the equations to eliminate the
xterm.
 
Answer

There is no solution.

http://www.montereyinstitute.org/courses/DevelopmentalMath/COURSE_TEXT2_RESOURCE/U14_L2_T2_text_final.html
Anatomy
Hormones
Although a given hormone may travel throughout the body in the bloodstream, it will affect the activity only of its target cells; that is, cells with receptors for that particular hormone. Once the hormone binds to the receptor, a chain of events is initiated that leads to the target cell’s response. Hormones play a critical role in the regulation of physiological processes because of the target cell responses they regulate. These responses contribute to human reproduction, growth and development of body tissues, metabolism, fluid, and electrolyte balance, sleep, and many other body functions. The major hormones of the human body and their effects are identified in [link].
Endocrine Glands and Their Major Hormones  

Endocrine gland  Associated hormones  Chemical class  Effect 
Pituitary (anterior)  Growth hormone (GH)  Protein  Promotes growth of body tissues 
Pituitary (anterior)  Prolactin (PRL)  Peptide  Promotes milk production 
Pituitary (anterior)  Thyroidstimulating hormone (TSH)  Glycoprotein  Stimulates thyroid hormone release 
Pituitary (anterior)  Adrenocorticotropic hormone (ACTH)  Peptide  Stimulates hormone release by adrenal cortex 
Pituitary (anterior)  Folliclestimulating hormone (FSH)  Glycoprotein  Stimulates gamete production 
Pituitary (anterior)  Luteinizing hormone (LH)  Glycoprotein  Stimulates androgen production by gonads 
Pituitary (posterior)  Antidiuretic hormone (ADH)  Peptide  Stimulates water reabsorption by kidneys 
Pituitary (posterior)  Oxytocin  Peptide  Stimulates uterine contractions during childbirth 
Thyroid  Thyroxine (T4), triiodothyronine (T3)  Amine  Stimulate basal metabolic rate 
Thyroid  Calcitonin  Peptide  Reduces blood Ca2+ levels 
Parathyroid  Parathyroid hormone (PTH)  Peptide  Increases blood Ca2+levels 
Adrenal (cortex)  Aldosterone  Steroid  Increases blood Na+ levels 
Adrenal (cortex)  Cortisol, corticosterone, cortisone  Steroid  Increase blood glucose levels 
Adrenal (medulla)  Epinephrine, norepinephrine  Amine  Stimulate fightorflight response 
Pineal  Melatonin  Amine  Regulates sleep cycles 
Pancreas  Insulin  Protein  Reduces blood glucose levels 
Pancreas  Glucagon  Protein  Increases blood glucose levels 
Testes  Testosterone  Steroid  Stimulates development of male secondary sex characteristics and sperm production 
Ovaries  Estrogens and progesterone  Steroid  Stimulate development of female secondary sex characteristics and prepare the body for childbirth 
Geometry
Find below the state study guide:
https://lorpub.gadoe.org/xmlui/bitstream/handle/123456789/50259/Milestones_StudyGuide_Geometry_4.19.17.pdf
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