## anonymous 5 years ago Please Help Me With This Problem, I Don't Quite Know How To Do It. . . What Is The Solution Of The System? Use Substitution. x=y-6 6x-3y=-9

1. anonymous

replace x in the second equation by y - 3, and get an equation with y alone $6(y-3)-3y=-9$

2. anonymous

then solve for y. don't forget the distributive law. $6y-18-3y=-9$ $3y-18=-9$ $3y=9$ $y=3$

3. anonymous

I Got 6y-18-3y=9. . Now What Can I Do ?

4. anonymous

Ohhh. Okay. Thank You Sooo Much!

5. anonymous

oops i made a mistake. it was y- 6 not y - 3

6. anonymous

i goofed. $6(y-6)-3y=-9$

7. anonymous

$6y-36-3y=-9$ $3y-36=-9$ $3y=27$ $y=9$

8. anonymous

now since $x=y-6$ and we know $y=27$ we get $x=27-6=21$

9. anonymous

10. anonymous

thank you, and no problem, thanks!♥

11. anonymous

welcome

12. anonymous

Wait. . But The Multiple Choice Says: A.(-2,-3) B.(-2-2.7) C.(-3,-2) D.(3,5) And 21 Isn't Either of those. . . .

13. anonymous

let me check see if i made a mistake

14. anonymous

Okay, And It Says To Eliminate, Not Substitute.

15. anonymous

ok yes i made a mistake. i wrote $y=9$ but then for some reason wrote $x=27-6$ instead of $x=9-6=3$

16. anonymous

my fault sorry. i do not know why i put y = 9 and then used y = 27 however, i am sticking with (3,9) and the check is easy: first equation x= y - 6 and 3 = 9 - 6 second equation is $6x-3y=-9$ and $6\times 3 - 3 \times 9 = 18-27=-9$

17. anonymous

so (3, 9) is right even if it is not one of the choices.

18. anonymous

elimination: rewrite $x=y-6$ as $x-y=-6$ and put $6x-3y=-9$ underneath so it looks like $x-y=-6$ $6x-3y=-9$

19. anonymous

if you want to eliminate the "y" multiply the top equation all the way across by -3 to get $-3x+3y=18$ $6x-3y=-9$

20. anonymous

that way when you add the "y"s will drop out to give $3x=9$ and so $x=3$

21. anonymous

dont forget to multiply EVERYTHING by the constant, otherwise you will not have the same equation.

22. anonymous

now you know $x=3$ you can substitute back to find y = 9. as before.

23. anonymous

Thank You!! (=