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damaskus [11]
3 years ago
10

HELP PLEASE!!!!! Solve each system.

Mathematics
2 answers:
Ede4ka [16]3 years ago
7 0

15.\ \text{Elimination method}\\\underline{+\left\{\begin{array}{ccc}y=-3x+9\\y=3x+3\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad2y=12\qquad\text{divide both sides by 2}\\.\qquad \boxed{y=6}\\\\\text{put the value of y to the second equation}\\\\6=3x+3\qquad\text{subtract 3 from both sides}\\3=3x\qquad\text{divide both sides by 3}\\1=x\to\boxed{x=1}\\\\Answer:\ x=1,\ y=6\to(1,\ 6)


16.\ \text{Substitution method}\\\left\{\begin{array}{ccc}y=11x+4\\y=7x-16\end{array}\right\Rightarrow11x+4=7x-16\\\\11x+4=7x-16\qquad\text{subtract 4 from both sides}\\11x=7x-20\qquad\text{subtract 7x from both sides}\\4x=-20\qquad\text{divide both sides by 4}\\\boxed{x=-5}\\\\\text{Put the value of x to the first equation}\\\\y=11(-5)+4\\y=-55+4\\\boxed{y=-51}\\\\Answer:\ x=-5,\ y=-51\to(-5,\ -51)

gogolik [260]3 years ago
7 0
15. -3x+9=3x+3
6x=-6
x=1
y=3x+3
y=6

16. 7x-16=11x+4
-20=4x
-5=x
y=-35-16
y=-51

do you understand? sorry if my english is bad i am Indonesian please corect me if i do some false
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" Vertical angles are congruent " ⇒ 2nd answer

Step-by-step explanation:

* <em>Look to the attached figure </em>

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∵ Line FA intersects line EC at point D

- The angles formed when two lines cross each other are called

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- Vertical angles are congruent (vertical angles theorem)

∴ ∠ADC and ∠FDE are vertical angles

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∴ ∠EDF ≅ ∠ADC

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∵ m∠BDC = (2x)° ⇒ given

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Column (1)                                                     Column (2)

m∠EDF = 120°                                               given

m∠ADB = 3 x                                                 given

m∠BDC = 2 x                                                 given

∠EDF and ∠ADC are vertical angles           defin. of vert. ∠s

∠EDF is congruent to ∠ADC                        vertical angles are      

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m∠ADC = m∠ADB + m∠BDC                        angle add. post.

m∠EDF = m∠ADC                                          defin. of cong.

m∠EDF = m∠ADB + m∠BDC                         substitution

120° = 3 x + 2 x                                               substitution

120 = 5 x                                                         addition

x = 24                                                              division  

∴ The missing reason is " vertical angles are congruent "

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