How do you solve #0.07 x - 0.01 y = 1.6 # and #0.26x + 0.18 y = 16.8# using substitution?

1 Answer
Apr 9, 2017

Answer:

# x = 30 # and # y = 50 #

Explanation:

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

# 0.07x - 0.01y = 1.6 # will become # -1.26x + 0.18y = -28.8 #

# 0.26x + 0.18y = 16.8 # will stay the same.

Now as you can see, both equations now have # 0.18y # in common. We will use this to substitute.

We will rewrite one equation, let's use the first one, to isolate # 0.18y #.

# -1.26x + 0.18y = -28.8 # will become # 0.18y = -28.8 + 1.26x #

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

# 0.26x + 0.18y = 16.8 #
# 0.26x + (-28.8 + 1.26x) = 16.8 #
# 0.26x - 28.8 + 1.26x = 16.8 #
# 1.52x - 28.8 = 16.8 #
# 1.52x = 45.6 #
# x = 30 #

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

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

# 0.07x - 0.01y = 1.6 #
# 0.07(30) - 0.01y = 1.6 #
# 2.1 - 0.01y = 1.6 #
# -0.01y = -0.5 #
# y = 50 #

So now we have solved the two equations to get # x = 30 # and # y = 50 #.