How do you solve the system of equations #-6x + 5y = - 5# and #10x - 10y = 20#?

1 Answer

Answer:

#x=-5# and #y=-7#.

Explanation:

For this system of equations, I would adjust the first equation so that when you add the two equations together, the #y# is eliminated.

You can do so by multiplying everything by #2#:

#(-6x+5y=-5)" " times 2#

#-12x+10y=-10#

Now that this equation has a positive #10y# and the other equation has a #-10y#, adding the two problems would eliminate the #y# variable.

#{(-12x+10y=-10), (10x -10y= 20) :}#

Added together:

#-2x=10#

You can now solve for #x# by dividing both sides by #-2#.

#x=-5#

Now you can take any of the equations and enter in #-5# for #x# to solve for #y#.

#-6(-5)+5y=-5#

Multiply the #-6# and #-5#

#30+5y=-5#

Subtract #30# from both sides

#5y=-35#

Divide both sides by #5#

#y=-7#

There are many ways to solve systems of equations, but often it's easiest to find a way to adjust one of the equations so that when you add them together they eliminate one of the variables.