1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Nina [5.8K]
3 years ago
9

This 1 seems really complicated

Mathematics
1 answer:
Fofino [41]3 years ago
7 0
The solution to this system set is:  "x = 4" , "y = 0" ;  or write as:  [4, 0] .
________________________________________________________
Given: 
________________________________________________________
 y = - 4x + 16 ; 

 4y − x + 4 = 0 ;
________________________________________________________
"Solve the system using substitution" .
________________________________________________________
First, let us simplify the second equation given, to get rid of the "0" ; 

→  4y − x + 4 = 0 ; 

Subtract "4" from each side of the equation ; 

→  4y − x + 4 − 4 = 0 − 4 ;

→  4y − x = -4 ;
________________________________________________________
So, we can now rewrite the two (2) equations in the given system:
________________________________________________________
   
y = - 4x + 16 ;   ===> Refer to this as "Equation 1" ; 

4y − x =  -4 ;     ===> Refer to this as "Equation 2" ; 
________________________________________________________
Solve for "x" and "y" ;  using "substitution" :
________________________________________________________
We are given, as "Equation 1" ;

→  " y = - 4x + 16 " ;
_______________________________________________________
→  Plug in this value for [all of] the value[s] for "y" into {"Equation 2"} ;

       to solve for "x" ;   as follows:
_______________________________________________________
Note:  "Equation 2" :

     →  " 4y − x =  - 4 " ; 
_________________________________________________
Substitute the value for "y" {i.e., the value provided for "y";  in "Equation 1}" ;
for into the this [rewritten version of] "Equation 2" ;
→ and "rewrite the equation" ;

→   as follows:  
_________________________________________________

→   " 4 (-4x + 16) − x = -4 " ;
_________________________________________________
Note the "distributive property" of multiplication :
_________________________________________________

   a(b + c)  = ab + ac ;   AND: 

   a(b − c) = ab <span>− ac .
_________________________________________________
As such:

We have:  
</span>
→   " 4 (-4x + 16) − x = - 4 " ;
_________________________________________________
AND:

→    "4 (-4x + 16) "  =  (4* -4x) + (4 *16)  =  " -16x + 64 " ;
_________________________________________________
Now, we can write the entire equation:

→  " -16x + 64 − x = - 4 " ; 

Note:  " - 16x − x =  -16x − 1x = -17x " ; 

→  " -17x + 64 = - 4 " ;   Solve for "x" ; 

Subtract "64" from EACH SIDE of the equation:

→  " -17x + 64 − 64 = - 4 − 64 " ;   

to get:  

→  " -17x = -68 " ;

Divide EACH side of the equation by "-17" ; 
   to isolate "x" on one side of the equation; & to solve for "x" ; 

→  -17x / -17 = -68/ -17 ; 

to get:  

→  x = 4  ;
______________________________________
Now, Plug this value for "x" ; into "{Equation 1"} ; 

which is:  " y = -4x + 16" ; to solve for "y".
______________________________________

→  y = -4(4) + 16 ; 

        = -16 + 16 ; 

→ y = 0 .
_________________________________________________________
The solution to this system set is:  "x = 4" , "y = 0" ;  or write as:  [4, 0] .
_________________________________________________________
Now, let us check our answers—as directed in this very question itself ; 
_________________________________________________________
→  Given the TWO (2) originally given equations in the system of equation; as they were originally rewitten; 

→  Let us check;  

→  For EACH of these 2 (TWO) equations;  do these two equations hold true {i.e. do EACH SIDE of these equations have equal values on each side} ; when we "plug in" our obtained values of "4" (for "x") ; and "0" for "y" ??? ; 

→ Consider the first equation given in our problem, as originally written in the system of equations:

→  " y = - 4x + 16 " ;    

→ Substitute:  "4" for "x" and "0" for "y" ;  When done, are both sides equal?

→  "0 = ?  -4(4) + 16 " ?? ;   →  "0 = ? -16 + 16 ?? " ;  →  Yes!  ;

 {Actually, that is how we obtained our value for "y" initially.}.

→ Now, let us check the other equation given—as originally written in this very question:

→  " 4y − x + 4 = ?? 0 ??? " ;

→ Let us "plug in" our obtained values into the equation;

 {that is:  "4" for the "x-value" ; & "0" for the "y-value" ;  

→  to see if the "other side of the equation" {i.e., the "right-hand side"} holds true {i.e., in the case of this very equation—is equal to "0".}.

→    " 4(0)  −  4 + 4 = ? 0 ?? " ;

      →  " 0  −  4  + 4 = ? 0 ?? " ;

      →  " - 4  + 4 = ? 0 ?? " ;  Yes!
_____________________________________________________
→  As such, from "checking [our] answer (obtained values)" , we can be reasonably certain that our answer [obtained values] :
_____________________________________________________
→   "x = 4" and "y = 0" ;  or; write as:  [0, 4]  ;  are correct.
_____________________________________________________
Hope this lenghty explanation is of help!  Best wishes!
_____________________________________________________
You might be interested in
(TIMED),<br> Which equation is represented in the graph?
AURORKA [14]

Answer:

y = e^x

Step-by-step explanation:

That curve represents a typical function of y = e^x, and to decide if it is y = e^x or y = e^x + 1 you need to replace x = 0

y = e^(0) = 1

y = e^(0) + 1 = 2

If you see the graph when x = 0, y = 1

So it is y = e^x

7 0
3 years ago
I need help with 5 and 6
8_murik_8 [283]

Answer:

w = 6

RS = 13

Step-by-step explanation:

RS + ST = RT

(2w + 1) + (w - 1) = 18

3w = 18

; w = 6

Hence the value of RS = 2(6) + 1

; RS = 13

AC = AB + BC

56 = (x + 16) + (5x + 10)

56 = 6x + 26....then rearrange the equation to form...;

56 - 26 = 6x

30 = 6x...

where...; x = 5

AB = 5 + 16 and BC = 5(5) + 10

;AB = 21 ;BC = 35

7 0
3 years ago
Help me plssssss I suck at this
Alex73 [517]

Answer: 7

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
I am learning about rate of change, please help
VashaNatasha [74]

Answer:

y=2

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
The arithmetic mean (average) of four numbers is 85. If the largest of these numbers is 97, find the mean of the remaining three
ser-zykov [4K]

Answer: 81

Step-by-step explanation:

Mean of four nos = 85

Score = 85 x 4 = 340

Deduct 97 from 340 = 243

Mean of three nos. 243/3 = 81

3 0
3 years ago
Other questions:
  • Simplify r2 –2r3 + 3r2
    15·1 answer
  • Simplify -3 square root of 84x^3
    6·1 answer
  • If the area of a circle is 154m2 what is the circumference.
    9·1 answer
  • Find the value of A<br> A: 18<br> B: 21<br> C: 20<br> D: 17
    12·2 answers
  • Y = 1.2 when x = 8<br> y varies inversely with x
    7·1 answer
  • Person 1 can do a certain job in twenty-one minutes, and person 2 can do the same job in twenty-eight minutes. When completing t
    14·1 answer
  • How do I solve?<img src="https://tex.z-dn.net/?f=2%20%3D%20%5Cfrac%7Bx%28x-1%29%28x-3%29%5E%7B2%7D%20%28x%2B1%29%7D%7Bx%7D" id="
    6·2 answers
  • You have 5 3/4 cups of sunflower seeds and 1 1/4 cups of peanuts for birdseed. You use 2/3 of the total mixture each week. How m
    10·1 answer
  • B<br> 16 m<br> A<br> С<br> 20 m -<br> Find the area of AABC.<br> [?] ml<br> Enter
    12·1 answer
  • How to write -1/2x + y=4 in slope form
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!