+0  
 
+2
55
5
avatar+439 

Solve the system of equations

 

5x-2y=16

15x-7y=51

 

 

Enter answer as ordered pair (x,y).

 

This is what I did:

 

-3(5x-2y=16)

 

-15x+6y=-48

15x-7y=51

--------------------

        y=3, then i knew that -7+6 is -y so then how does that change the 3??????

       

Substitute the y

 

5x-2(3)=16

5x-6=16

     +6 +6

5x=22

/5    /5

x=22/5

 

(22/5,3)

 

Do you know what I did. I saw that -7+6 is -y=3 so how does that change the answer. Btw the answer (22/5,3) is wrong. Could you help me.

 

Thank you.

 Sep 30, 2021
 #1
avatar+114832 
+2

ok, your first step is fine

 

Solve the system of equations

 

5x-2y=16

15x-7y=51

 

 

Enter answer as ordered pair (x,y).

 

This is what I did:

 

-3(5x-2y=16)

 

-15x+6y=-48

15x-7y=51

 

so far so good  :)

   I am going to sid track for a bit

        You know that   24 = 2 dozen

        and you know that    7 = 21/3

        these are completely unrelated facts but from this knowledge I can say   24+7 = 2 dozen + 21/3

        Think very hard about what I have done.  I added the left sides and that will = the sum of the right side.

So

you have

-15x+6y=-48

15x-7y=51

 

these are 2 independent facts

Add the left sides and that will equal the sum of the right sides

-15x+15x+6y+-7y = -48+51

-1y=3

y=-3

 

Now you know that y=-3 just sub it into one of the original equations to get x

5x-2y=16

5x-2*-3=16

5x+6=16

5x=10

x=2

 

so I have x=2 and y = -3

 

I have substituted them into both original equations to check and they work just fine.

 

Your second question you have asked is almost identical.   Just easier.

https://web2.0calc.com/questions/consider-the-system-of-equations_2

Learn from what I have written and try answering it for yourself    laugh

 Sep 30, 2021
 #2
avatar+439 
+1

Thank you, it helps. But I dont understnad how the answer could help me find my second question, it tells me to substitute but it doesn't give deep details about the question.

 Sep 30, 2021
 #3
avatar+35058 
+2

Solve the system of equations

 

5x-2y=16     <===== multiply this equation by -3 to get

-15x+6y= - 48     now add to the other equation ( the 15x will cancel out)

15x-7y=51

      - y = 3

        y = -3      now sustitute this value of y into any of the equations to calculate the value of 'x'

 Sep 30, 2021
 #4
avatar+439 
+2

Thank you EP. I will surely "SUStitute" the y for the x. XD :)

 Sep 30, 2021
edited by weredumbmaster22  Sep 30, 2021
 #5
avatar+35058 
+1

  What can I say.... I can't type worth a dhit .... haha

ElectricPavlov  Sep 30, 2021

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