Question

Find one possible missing coordinate so that the point becomes a solution to the given inequality. (x,4) is a solution to 4x−4≤y.

Answer 1

For (x,4) to be a solution.

Given:

`4x-4\le y`
`\begin{gathered} (x,4)\text{ is a solution, then it implies,} \\ y=4 \\ \\ \text{substituting y=4 into the inequality,} \\ 4x-4\le y \\ 4x-4\le4 \\ 4x\le4+4 \\ 4x\le8 \\ \text{Dividing both sides by 4,} \\ x\le(8)/(4) \\ x\le2 \\ \\ \text{This implies for (x,4) to become a solution, x must be a value less than or equal to 2.} \\ \\ \text{Hence, the possible values of x are;} \\ \mleft\lbrace\ldots\text{.,}-3,-2,-1,0,1,2\mright\rbrace \end{gathered}`

Thus, a possible missing coordinate of x to make the point (x,4) a solution is;

`\begin{gathered} x=2 \\ \\ \text{Then point (2,4) is a solution to 4x-4}\leq y \end{gathered}`