Question

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.

Answer 1

do you know the method of substitution?

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

and then solve for x

Answer 6

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

Answer 7

you can work analogous in your problem

Answer 8

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?

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

*explaining

Answer 14

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:\[y=-\frac{ 4 }{ 21 }\]

Answer 15

Hope it help

Answer 16

thank you