How do solve the following linear system?: #-4x + 9y = 9 , -3x + 7y= -16 #?

We will solve this using substitution (although you can solve it with other methods, I prefer this one).

First, we must rewrite the two equations and make sure they have an identical term. I will rewrite them as follows:

# -4x + 9y = 9 # will become # -12x + 27y = 27 #

# -3x + 7y = -16 # will become # -12x + 28y = -64 #

Now as you can see, both equations now have # -12x # in common. We will use this to substitute.

We will rewrite one equation, let's use the first one, to isolate # -12x #.

# -12x + 27y = 27 # will become # -12x = 27 - 27y #

Now we can substitute this into the second equation to find the first variable.

# -12x + 28y = -64 #
# (27 - 27y) + 28y = -64 #
# 27 - 27y + 28y = -64 #
# 27 + y = -64 #
# y = -91 #

Now that we have found the value of # y #, we can move on to substitute this value to find # x #.

Take an original question, we'll use the first one, and substitute our # y # value.

# -4x + 9y = 9 #
# -4x + 9 (-91) = 9 #
# -4x - 819 = 9 #
# -4x = 828 #
# x = -207 #

So now we have solved the two equations to get # y = -91 # and # x = -207 #.