Respuesta :
x= 0 y=8
or
x=1 y=9
Explanationgiven the equation of the line
[tex]4x-4y=-32[/tex]Step 1
a) isolate y to obtain the slope intercept form
so
[tex]\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} \\ \frac{-4y}{-4}=\frac{-32-4x}{-4}=\frac{-32}{-4}-\frac{4x}{-4} \\ y=8+x \\ y=x+8 \end{gathered}[/tex]b) now, we can input values to obtain ordered pairs
hence
i) for x= 0 ( you can choose any value)
replace
[tex]\begin{gathered} y=x+8 \\ y=0+8 \\ y=8 \\ so,\text{ the pair is x=0 y=8} \end{gathered}[/tex]to prove it, let's replace in the original equation :
[tex]\begin{gathered} 4x-4y=-32 \\ 4(0)-4(8)=-32 \\ -32=-32\Rightarrow true \end{gathered}[/tex]ii) for x= 1
replace
[tex]\begin{gathered} y=x+8 \\ y=1+8 \\ y=9 \\ so,\text{ the pair is x=1 y=9} \end{gathered}[/tex]to prove it, let's replace in the original equation :
[tex]\begin{gathered} 4x-4y=-32 \\ 4(1)-4(9)=-32 \\ 4-36=-32\Rightarrow true \end{gathered}[/tex]so we have 2 solutions, the ordered pairs are
x= 0 y=8
or
x=1 y=9
I hope this helps you
