SOLUTION: Solve the system of equations 8x + 4y = 8 -12x + 3y = 12 a) symbolically b) graphically c) numerically Can someone assist me with this. I need to see how the solution w

Algebra ->  Graphs -> SOLUTION: Solve the system of equations 8x + 4y = 8 -12x + 3y = 12 a) symbolically b) graphically c) numerically Can someone assist me with this. I need to see how the solution w      Log On


   

Question 459937: Solve the system of equations
8x + 4y = 8
-12x + 3y = 12
a) symbolically
b) graphically
c) numerically
Can someone assist me with this. I need to see how the solution was arrived at.
Thank you in advance for your assistance.
Devoted,
Minka.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
: Solve the system of equations
8x + 4y = 8
-12x + 3y = 12
:
multiply the the 1st equation by 1.5, use elimination here
12x + 6y = 12
-12x+ 3y = 12
--------------adding eliminates x, find y
9y = 24
y = 24%2F9
y = 8%2F3
:
Use the 2nd equation to find x, replace y with 8/3
-12x + 3(8%2F3) = 12
-12x + 8 = 12
-12x = 12 - 8
x = 4%2F-12
x = -1%2F3
:
therefore solution is: x = -1%2F3, y = 8%2F3
Is this symbolically or numerically? I don't know.
:
But graphically, put both equations in the slope/intercept form
8x + 4y = 8
4y = -8x + 8
Divide by 4
y = -2x + 2; (red)
and
-12x + 3y = 12
3y = 12x + 12
divide by 3
y = 4x + 4, (green)
:
Graph these two equations, should look like this
+graph%28+300%2C+200%2C+-4%2C+4%2C+-4%2C+6%2C+-2x%2B2%2C+4x%2B4%29+
:
Note the intersection is x = -1%2F3, y = 8%2F3
:
Minka is a great name!