Can you please help?

At a store, you can buy three packs of heavy duty batteries and six boxes of cereal for $48.00. You can also buy two packs of heavy-duty batteries and eight boxes of cereal for $46.00. What is the cost of one pack of heavy duty batteries at this store.

3x +6y = $48.00
2x + 8y = $46.00

3 (3x + 7y )=144
9x + 21y = 144

2 (2x + 8y) =92
4x + 16y =92

is this all incorrect?

1 answer

don't make it so complicated, all you want is the coefficients of either the x's or the y's to be the same.

3x +6y = $48.00 , divide by 3 --> x + 2y = 16
2x + 8y = $46.00 , divide by 2 --> x + 4y = 23

subtract them:
2y = 7
y = 3.5
then in x+2y = 16
x + 7 = 16
x = 9