Lori bought a shirt and a hat at a half off sale and she spent a total of 21$ if the shirt was originally 24 how much was the original price of the hat

Step-by-step explanation:

$21

Let the amount Lori bought the shirt and the hat be $x, if she bought them at half off sale, the initial price of both item will be 2 × $x

If she spent $21 on both items, the initial price will have been 2 x $21 = $42 where x is $21

Original price of the hat and shirt is therefore $42. Since both are on half off sale, the initial price is the hat will be $42/2 = $21

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1