Question

Complete the table of values for 2 x - 5 y =10

Answer 1

x y

0 -2

1 -8/5

-2 -14/5

2 -6/5

Step-by-step explanation

We can solve the equation for y. First add 5y to both sides of the equation:

`\begin{gathered} 2x-5y+5y=10+5y \\ 2x=10+5y \end{gathered}`

Then subtract 10 from both sides:

`\begin{gathered} 2x-10=10-10+5y \\ 2x-10=5y \end{gathered}`

And divide both sides by 5:

`(2)/(5)x-2=y`

And we can flip the equation so we read the y first:

`y=(2)/(5)x-2`

Now, to complete the table we have to replace x by each of its values in the equation above and solve to find the y-value:

`y=(2)/(5)0-2=0-2=-2`
`y=(2)/(5)\cdot1-2=(2)/(5)-2=-(8)/(5)`
`y=(2)/(5)\cdot(-2)-2=-(4)/(5)-2=-(14)/(5)`
`y=(2)/(5)\cdot2-2=(4)/(5)-2=-(6)/(5)`