Question

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

Answer 1

`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`.