How do you solve 0.07 x - 0.01 y = 1.6 0.07x0.01y=1.6 and 0.26x + 0.18 y = 16.80.26x+0.18y=16.8 using substitution?

1 Answer
Apr 9, 2017

x = 30 x=30 and y = 50 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 0.07x0.01y=1.6 will become -1.26x + 0.18y = -28.8 1.26x+0.18y=28.8

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

Now as you can see, both equations now have 0.18y 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 0.18y.

-1.26x + 0.18y = -28.8 1.26x+0.18y=28.8 will become 0.18y = -28.8 + 1.26x 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+0.18y=16.8
0.26x + (-28.8 + 1.26x) = 16.8 0.26x+(28.8+1.26x)=16.8
0.26x - 28.8 + 1.26x = 16.8 0.26x28.8+1.26x=16.8
1.52x - 28.8 = 16.8 1.52x28.8=16.8
1.52x = 45.6 1.52x=45.6
x = 30 x=30

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

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

0.07x - 0.01y = 1.6 0.07x0.01y=1.6
0.07(30) - 0.01y = 1.6 0.07(30)0.01y=1.6
2.1 - 0.01y = 1.6 2.10.01y=1.6
-0.01y = -0.5 0.01y=0.5
y = 50 y=50

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