## anonymous one year ago Can someone help me with substitution? Anyone?

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1. sepeario

No problems.

2. pooja195

Hi there! Welcome to Openstudy! :D Please post your question so that we can assist u :)

3. anonymous

Y=5x-7 Y=3/2x+6

4. sepeario

Okay if you have that and we know that obviously y=y then we can also show that 5x-7=3/2x+6, correct?

5. sepeario

Okay if you have that and we know that obviously y=y then we can also show that 5x-7=3/2x+6, correct? $5x-7=\frac{ 3 }{ 2x }+6$

6. sepeario

Can you then solve for x?

7. pooja195

Ok well when we use the susbtistuion mthod we basically substitue a given value into one of the equations lets call Equation A - Y=5x-7 Equation B-Y=3/2x+6 Y value is given you can sub either equation into each other for now lets sub equation A into equation B $\huge~\rm~5x-7=3/2x+6$

8. pooja195

Now all you do is solve for x if you need help with that ill be glad to help ^_^

9. anonymous

How would I solve for x though? First I know I could add 7 to both sides making the equation 5x=3/2x+13 but then idk how to cancel the x's

10. pooja195

well subtract the x's from both side :) 5x-3/2x=?

11. anonymous

But wait XD the x is connected to the 3/2 fraction. You can't subtract it 😭

12. pooja195

ignore the x's for now

13. sepeario

lol k

14. pooja195

5-3/2=?

15. anonymous

Hmmm but then 3/2 is still a fraction tho O:

16. pooja195

You can subtract fraction :o did u know that?? :D

17. anonymous

Hmmm but then 3/2 is still a fraction tho O:

18. pooja195

o.O

19. anonymous

LOL MY BAD. would it be like 5/1 - 3/2?

20. anonymous

LOL MY BAD. would it be like 5/1 - 3/2?

21. pooja195

ok let me just explain this one to u Ok well when we use the substitution method we basically substitute a given value into one of the equations lets call Equation A - Y=5x-7 Equation B-Y=3/2x+6 Y value is given you can sub either equation into each other for now lets sub equation A into equation B $\huge~\rm~5x-7=3/2x+6$ We add 7 to both sides $$\huge\color{red}{5x=3/2x+13}$$ Then we subtract x's from both sides For x we get 26/7 Then we substitute the value of x into Equation A $\huge~\rm~5(26/7)-7$ Once you simplify you get y=81/7

22. pooja195

(26/7,81/7)

23. anonymous

How did you get 26/7 (sorry I just really don't understand) 😭😭😭😭

24. mathstudent55

$$y=5x-7$$ $$y=\dfrac{3}{2}x+6$$ Since y = y, we can set the right sides equal to each other and solve for x. $$5x - 7 = \dfrac{3}{2}x + 6$$ $$5x - \dfrac{3}{2}x + 13$$ $$\dfrac{10}{2}x - \dfrac{3}{2}x = 13$$ $$\dfrac{7}{2} x = 13$$ $$x = \dfrac{26}{7}$$ Now that we know what x is, we plug in the value we have for x into the first original equation to find y. $$y = 5(\dfrac{26}{7}) - 7$$ $$y = \dfrac{130}{7} - \dfrac{49}{7}$$ $$y = \dfrac{81}{7}$$

25. pooja195

Thats what i did

26. mathstudent55

@Pooja195 You wrote: "We add 7 to both sides 5x=3/2x+13 Then we subtract x's from both sides For x we get 26/7" I'm not as smart as you, so it takes me a few more steps than it took you to find what x was equal to. Since the poster asked how you got 26/7 for x, I thought I'd show the extra steps it took me to find x.

27. pooja195

Never said i was a smart person. Just didnt realize the difference thanks for explaining.