During one month, a homeowner use 600 units of electricity and 100 units of gas for total cost of $412. the next month, 400 units of electricity and 150 units of gas for used for total cost of $293. find the cost per unit of gas

This is a simultaneous question.
To solve this, we have to make up 2 equations based on the info provided like so:

electricity = e
gas = g

600e + 100g = $412 ——(1)
400e + 150g = $293 ——(2)

In this case, it’ll be easier to use the elimination method where you eliminate a variable so you can calculate only one.

Here, we will be eliminating e so we can get the cost of gas.

To do this we need to get both equation’s e to 600, so we have to multiply equation 2 by 1.5:

(2) x 1.5:

400e + 150g = $293
600e + 225g = $439.50 ——(3)

Now we eliminate e by subtracting equation 1 from equation 3:

(3) - (1):
600e + 225g - 600e - 100g = $439.50 -$412

125g = $27.50
g = $0.22.

Therefore one unit of gas costs $0.22.

Hope it helps and have a good day ahead :D