At a sale on winter clothing, cody bought two pairs of gloves and four hats for $43.00. tori bought two pairs of gloves and two hats for $30.00. what were the prices for the gloves and hats?

Let g = number of gloves and let h = number of hats. We're going to write a system of equations.
2g+4h=43
2g+2h=30
Now I'm going to isolate a variable in one of the equations. Let's isolate the g in the second equation
g+h=15
g=15-h
Next, I'm going to plug in my new equation for g into the first equation and solve for h.
2(15-h)+4h=43
30-2h+4h=43
30+2h=43
2h=13
h=6.5
Finally, I'm going to plug my solution for h into either equation (I'll use the second one) and solve for g.
2g+2(6.5)=30
2g+13=30
2g=17
g=8.5
If I want to double check my answers, I can plug both values into the first equation and see if I get 43. The hats are $6.50 and the gloves are $8.50.

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