Math help requiring algebra 1

(This problem is fictional) Bags of hugs hersheys sell for $4 each and bags of kisses sell for $5 each. Ms. Holmes purchased 10 bags total and spent $44. How many bags of each kind of chocolate did she buy?
I am just looking for the 2 equations to solve it but if u want to solve it that is fine too.

let
x = number of bags of hugs
y = number of bags of kisses

x + y = 10
4x + 5y = 44

First we need an expression for the cost of the hugs hershey. We don't know how many bags of hugs hershey Ms. Holmes bought so lets say she bought x bags. Each bag is $4 so the total cost is 4 * number of bags of hugs hershey = cost. Well we just said the number of bag is x, so the cost is 4x. Lets call the number of bags of kisses is y. The cost would be 5y then, based on what we did earlier. So now we have everything we need to get two equations. One equation would be cost, the other how many bags so let's set them up.

Cost of Hugs + Cost of Kisses = 44
4x + 5y = 44

Number of Hugs + Number of Kisses = 10
x + y = 10

Our equations are therefore
4x + 5y = 44
x + y = 10

I'm not going to solve this for you, I think you should try it yourself. However so you can check your answer later the solution is 6 bags of hugs and 4 bags of kisses.

Step 1: Let x= number of bags of kisses
let y= number of bags of hugs

Step 2.

x + y = 10
5x+4y=44

Step 3.

Multiply top equation by 5

5x + 5y = 50
5x + 4y = 44

Step 4.

Subtract: 1y = 6

Step 5.

Divide by 1

Step 6.

Answer: y=6

then add in 6 to the equation,

x + 6= 10

x= 4

Overall answer: (4,6)

4x+5y=44