We have the following system of equations,
[tex]
\begin{cases}
8x+2y=6 \\
2x+3y=9 \\
\end{cases}
[/tex]
We have to find the intersection of these two lines namely point [tex]P(x,y)[/tex].
Use elimination method to solve this system of equations.
Multiply the first equation by 3 and second equation by -2 to get,
[tex]
\begin{cases}
24x+6y=18 \\
-4x-6y=-18
\end{cases}
[/tex]
Add the equations and obtain,
[tex]20x=0\implies x=0[/tex].
Now plug in the 0 we just obtained to one of the original equations, note that I will insert the value in first one to get,
[tex]2y=6\implies y=3[/tex].
So the solution is point [tex]P(0,3)[/tex].
Hope this helps.
Answer:
x = 0 and y = 3 respectively
Step-by-step explanation:
in order to solve this system of equation we would say that let
8x+2y=6...........................................................................equation 1
2x+3y=9 ...........................................................................equation 2
from equation 1
8x+2y=6...........................................................................equation 1
2y = 6 - 8x
divide both sides by 2
2y/2 = 6-8x/2
y = ( 6- 8x)/2.................................................................. equation 3
substitute for equation 3 in equation 2
2x+3y=9 ...........................................................................equation 2
2x + 3 [( 6 - 8x)/2] = 9
2x + (18 - 24x )/2 = 9
multiply through by 2
4x + 18 -24x = 18
collect the like terms
24x - 4x = 18 -18
20x = 0
divide both sides by 20
20x/20 = 0/20
x = 0
put the value of x = 0 into equation 3
y = ( 6- 8x)/2.................................................................. equation 3
y = 6 - 8(0) / 2
y = 6 - 0/2
y = 6/2
y = 3
therefore the value of x = 0 and y = 3 respectively
