Chapter 3.7, Problem 53E

To determine

To find: the coordinate which satisfy the given equation.

Answer to Problem 53E

The coordinate does not satisfy the equation.

Explanation of Solution

Given:

Equation is:

  $x+y=8.$

The coordinate is:

  $\left(0,9\right),\left(-1,2\right),\left(-4,2\right),\left(-2,4\right)$ .

Concept used:

By putting the value or coordinate to the equation can check whether the coordinate satisfy the equation.

If it’s satisfy the equation then the point is solution of the equation.

Calculation:

The inequality is:

  $x+y=8.$

Now, it has to check the inequality $\left(i\right)$ for $x\text{ and }y$ of:

  $\left(0,9\right),\left(-1,2\right),\left(-4,2\right),\left(-2,4\right)$ .

For $\left(0,9\right)$ :

  $\begin{array}{l}0+9=8.\\ 9\ne 8.\end{array}$

Which is not true.

For $\left(-1,2\right)$ ;

  $\begin{array}{l}-1+2=8.\\ 1\ne 8.\end{array}$

Which is true.

For $\left(-4,2\right)$ ;

  $\begin{array}{l}x+y=8.\\ -4+2=8.\\ -2\ne 8.\end{array}$

Which is not true.

For $\left(-2,4\right)$ ;

  $\begin{array}{l}-2+4=8.\\ 2\ne 8.\end{array}$

Which is not true.

Hence, the coordinate does not satisfy the equation.