## anonymous one year ago Given the system of equations: y  =  3 x  +  9  4 x − 9 y  =  − 8 Find the  y-coordinate of the point of intersection of the two lines.

1. TheSmartOne

do you know the method of substitution?

2. anonymous

method of substitution is when you plug one equation into another?

3. EmmaTassone

If you want to see the intersection point you have to look for the point that comply both equation. e.g. if I have this system: a) x+y=1 b) x-y=0 and i want to find now y-coordinate that comply the equations, so from b) we have x=y so we replace this information in a) then : x+x=1 ==> 2x=1 ====> x=1/2 since x=y ===> Y=1/2 in my example

4. TheSmartOne

yes, you can plug in the first equation in to the second one

5. TheSmartOne

and then solve for x

6. TheSmartOne

then plug in the value you got for x into any of those equations and solve for y

7. EmmaTassone

you can work analogous in your problem

8. anonymous

which one is easier? I am not sure where emma got the 2x from here example. came from. If I plug one equation into another do I plug it into the front or back?

9. EmmaTassone

i used the substitution method xD i just plug the y=x in the other equation

10. EmmaTassone

you have to clear a variable first and then plug that variable in the other equation

11. EmmaTassone

I can do the example again exaplining it better if you want

12. anonymous

I am not sure where I put the y= 3x + 9 ... into 4x-9y=-8

13. EmmaTassone

*explaining

14. EmmaTassone

Here its another example with this system: $4x+6y=0$ $5x=3y+2$ So, what you have to do is clear one variable from any equation, im going to clear variable x from first equation:$4x+6y=0 \rightarrow 4x=-6y \rightarrow x=\frac{ -6 }{ 4 }.y$ Once we cleared x, we plug it in the second equation:$5x=3y+2$ replacing it: $5(\frac{ -6 }{ 4 }.y)=3y+2$ $\frac{ -30 }{ 4 }.y=3y+2$ $-\frac{ 30 }{ 4 }y-3y=2$ $-\frac{ 21 }{ 2 }y=2$ Finally:$y=-\frac{ 4 }{ 21 }$

15. EmmaTassone

Hope it help

16. anonymous

thank you