How do solve the following linear system?: # -6x+5y=1 , 6x+4y=-1 #?

Question

How do solve the following linear system?: #  -6x+5y=1  ,  6x+4y=-1   #?

Ethan Adkins · Accepted Answer

#color(magenta)(x=-1/6 and y=0#

Adding both the equations:

#-cancel(6x)+5y+cancel(6x)+4y=1-1#

#9y=0#

#color(red)(y=0#

Given that,

#6x+4y=-1#

#6x+4xx0=-1#

#6x=-1#

#color(red)(x=-1/6#

#therefore# #color(magenta)(x=-1/6 and y=0#

~Hope this helps! :)

Ethan Adkins · Answer

undefined To solve the linear system:
-6x + 5y = 1
6x + 4y = -1

You can use the method of elimination or substitution.

Using elimination:
1. Multiply the first equation by 6 and the second equation by -6 to eliminate the variable x.
   -36x + 30y = 6
   -36x - 24y = 6
2. Add the equations together to eliminate x:
   (30y - 24y) = 6 + (-1)
   6y = 5
3. Solve for y:
   y = 5/6

Using substitution:
1. Solve one equation for one variable, say the first equation for x:
   -6x = -5y + 1
   x = (5y - 1)/6
2. Substitute this expression for x into the second equation:
   6((5y - 1)/6) + 4y = -1
3. Solve for y:
   5y - 1 + 4y = -1
   9y - 1 = -1
   9y = 0
   y = 0
4. Substitute the value of y back into one of the original equations to solve for x:
   -6x + 5(0) = 1
   -6x = 1
   x = -1/6

So, the solution to the system is x = -1/6 and y = 5/6.