Question

O GRAPHS AND FUNCTIONSIdentifying solutions to a linear equation in two variables

Answer 1

Given:

Function is:

`9x+2y=13`

Find-:

Check for solution

Explanation-:

The value of "y" is:

`\begin{gathered} 9x+2y=13 \\ \\ 2y=13-9x \\ \\ y=(13-9x)/(2) \end{gathered}`

For (0,8)

Check value of "y" at x = 0 then,

`\begin{gathered} x=0 \\ \\ y=(13-9x)/(2) \\ \\ y=(13-9(0))/(2) \\ \\ y=(13-0)/(2) \\ \\ y=(13)/(2) \\ \\ y=6.5 \end{gathered}`

So (0,8) it is not a solution.

Check (3,-7) the value of "x" is 3

`\begin{gathered} x=3 \\ \\ y=(13-9x)/(2) \\ \\ y=(13-9(3))/(2) \\ \\ y=(13-27)/(2) \\ \\ y=-(14)/(2) \\ \\ y=-7 \end{gathered}`

So (3,-7) is the solution of function.

Check for (1 , 2) value of "x" is 1.

`\begin{gathered} x=1 \\ \\ y=(13-9x)/(2) \\ \\ y=(13-9)/(2) \\ \\ y=(4)/(2) \\ \\ y=2 \end{gathered}`

So, (1,2) is the solution.

Check for (4,-5) the value of "x" is 4.

`\begin{gathered} x=4 \\ \\ y=(13-9x)/(2) \\ \\ y=(13-9(4))/(2) \\ \\ y=(13-36)/(2) \\ \\ y=-(23)/(2) \\ \\ y=-11.5 \end{gathered}`

So, (4,-5) is not a solution