Question

An integer solution to the equation 3x + 4 = 7y is an ordered pair of integers (x, y) that satisfies the equation. For example, (1, 1) is one such solution. Write the set of all integer solutions to the equation 3x + 4 = 7y in set builder notation.

Answer 1

`\3x+4=7y\`

Explanation:

The given equation is

`3x+4=7y`

An integer solution to the given equation is an ordered pair of integers (x, y) that satisfies the equation.

We need to write the set of all integer solutions to the given equation in set builder notation. It means x and y both are integers

`x\in Z, y\in Z`

`(x,y)\in Z* Z`

Solution (x,y) musty be satisfy the equation 3x+4=7y. So, the set builder form is

`Solution=\(x,y)\in Z* Z`

Therefore, the set of all integer solutions to the equation 3x + 4 = 7y in set builder notation is
`\3x+4=7y\`.