Chapter 8.4, Problem 25SR

To determine

To find: four solution and write in a table of ordered pairs.

Answer to Problem 25SR

The complete table that shows different value of x and y is as follow:

x	y
-1	-13
0	-10
1	-7
2	4

And, the four ordered pair solution of the equation $3x-y=10$ is:

  $\left(-1,-13\right),\left(0,–10\right),\left(1,-7\right),\left(2,-4\right)$

Explanation of Solution

Given:

Consider the equation: $3x-y=10$

Calculation:

First step is to separate the variable y

Add both sides of equation by y

  $\begin{array}{l}3x-y+y=10+y\\ 3x=10+y\end{array}$

Subtract both sides of equation by 10

  $\begin{array}{l}3x-10=10+y-10\\ 3x-10=y\end{array}$

Take different value of x and solve for y

Put $x=-1$ in equation.

  $\begin{array}{l}\begin{array}{l}y=3\left(-1\right)-10\hfill \\ =-3-10\hfill \end{array}\\ =-13\end{array}$

Now, put $x=0$ in equation.

  $\begin{array}{l}\begin{array}{l}y=3\left(0\right)-10\hfill \\ =0-10\hfill \end{array}\\ =-10\end{array}$

Put $x=1$ in equation.

  $\begin{array}{l}\begin{array}{l}y=3\left(1\right)-10\hfill \\ =3-10\hfill \end{array}\\ =-7\end{array}$

Put $x=2$ in equation

  $\begin{array}{l}y=3\left(2\right)-10\hfill \\ =6-10\hfill \\ =-4\hfill \end{array}$

Conclusion:

Therefore, the complete table that shows different value of x and y is as follow:

x	y
-1	-5
0	-3
1	-1
2	1

And, the four ordered pair solution of the equation $y\text{ = }2x-3$ is:

  $\left(-1,-5\right),\left(0,–3\right),\left(1,-1\right),\left(2,1\right)$