Question

How do you solve the system `y= 1.2x - 46` and `y = 0.6x - 0.22` by substitution?

Answer 1

Choose one equation to solve for one of the variables in terms of the other variable (your choice). Substitute the solution you get into the other equation.

`y=1.2x-46`
`y=0.6x-0,22`

I choose to solve the first equation for `y` in terms of `x` (because it is already solved for `y` in terms of `x`!)
`y=1.2x-46`

Now replace any `y`'s in the second equation with `1.2x-46`

We get:

`1.2x-46 = 0.6x-0.22`

Solve for `x`.

`1.2x-0.6x = 46-0.22`

`0.6x = 45.78`

`x = 45.78/0.6` (if you have a calculator, you can use it)

`x = 45.78/0.6 = 45.78/(6/10) = 45.78*(10/6) = 457.8/6 = 76.3`

Finally, finish by finding `y`.
We already "solved" the first equation for `y` in terms of `x`
`y=1.2x-46`.

So in the solution, `y = 1.2(76.3)-46 = 45.56`

The solution is:

`x = 76.3` and `y = 45.56`.