Question

Find a pair of values that make the linear equation 4x – 4y = -32 a true statement by filling in the boxes with a validvalue of x and y.

Answer 1

x= 0 y=8

or

x=1 y=9

Step-by-step explanation

given the equation of the line

`4x-4y=-32`

Step 1

a) isolate y to obtain the slope intercept form

so

`\begin{gathered} 4x-4y=-32 \\ subtract\text{ 4x in both sides} \\ 4x-4y-4x=-32-4x \\ -4y=-32-4x \\ divide\text{ both sides by -4 and order} \\ (-4y)/(-4)=(-32-4x)/(-4)=(-32)/(-4)-(4x)/(-4) \\ y=8+x \\ y=x+8 \end{gathered}`

b) now, we can input values to obtain ordered pairs

hence

i) for x= 0 ( you can choose any value)

replace

`\begin{gathered} y=x+8 \\ y=0+8 \\ y=8 \\ so,\text{ the pair is x=0 y=8} \end{gathered}`

to prove it, let's replace in the original equation :

`\begin{gathered} 4x-4y=-32 \\ 4(0)-4(8)=-32 \\ -32=-32\Rightarrow true \end{gathered}`

ii) for x= 1

replace

`\begin{gathered} y=x+8 \\ y=1+8 \\ y=9 \\ so,\text{ the pair is x=1 y=9} \end{gathered}`

to prove it, let's replace in the original equation :

`\begin{gathered} 4x-4y=-32 \\ 4(1)-4(9)=-32 \\ 4-36=-32\Rightarrow true \end{gathered}`

so we have 2 solutions, the ordered pairs are

x= 0 y=8

or

x=1 y=9

I hope this helps you