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.

weredumbmaster22 Sep 30, 2021

#1**+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

Melody Sep 30, 2021

#2**+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.

weredumbmaster22 Sep 30, 2021

#3**+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'

ElectricPavlov Sep 30, 2021