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.

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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.

Mathematics
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do you know the method of substitution?
method of substitution is when you plug one equation into another?
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

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Other answers:

yes, you can plug in the first equation in to the second one
and then solve for x
then plug in the value you got for x into any of those equations and solve for y
you can work analogous in your problem
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?
i used the substitution method xD i just plug the y=x in the other equation
you have to clear a variable first and then plug that variable in the other equation
I can do the example again exaplining it better if you want
I am not sure where I put the y= 3x + 9 ... into 4x-9y=-8
*explaining
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:\[y=-\frac{ 4 }{ 21 }\]
Hope it help
thank you

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