The cost of 2 televisions and 3 DVD players is $1,421. The cost of 1DVD player is half the cost of 1 television. What is the cost of 1 television?

$X = Cost of each TV.

$X/2 = Cost of each DVD.

2x + 3x/2 = 1421
Multiply both sides by 2:
4x + 3x = 2842
7x = 2842
X = $406 = Cost of 1 TV.

Let's start by assigning variables to the unknowns. Let's say the cost of 1 television is "x" dollars. According to the given information, the cost of 1 DVD player is half the cost of 1 television. Therefore, the cost of 1 DVD player is "0.5x" dollars.

We are also given that the cost of 2 televisions and 3 DVD players together is $1,421. Therefore, we can set up the following equation:

2x + 3(0.5x) = 1421

Simplifying the equation:

2x + 1.5x = 1421
3.5x = 1421
x = 1421 / 3.5

Evaluating the expression:

x ≈ 406

Therefore, the cost of 1 television is approximately $406.

To find the cost of 1 television, we can set up a system of equations based on the given information.

Let's denote the cost of 1 television as "T" and the cost of 1 DVD player as "D".

According to the problem, the cost of 2 televisions and 3 DVD players is $1,421, so we can write the equation:

2T + 3D = 1421

The problem also states that the cost of 1 DVD player is half the cost of 1 television, so we can set up another equation:

D = 0.5T

Now we have a system of equations:

2T + 3D = 1421
D = 0.5T

We can use substitution method or elimination method to solve this system of equations. Let's use substitution method.

Since D = 0.5T, we can substitute this expression into the first equation:

2T + 3(0.5T) = 1421

Simplifying the equation:

2T + 1.5T = 1421
3.5T = 1421
T = 1421 / 3.5
T ≈ $405.71

Therefore, the cost of 1 television is approximately $405.71.