Answer :
Hello there!
The question asks us to solve using the substitution method. The equations given are:
[tex]2x+3y=1[/tex]
[tex]y=x-8[/tex]
We are given a value for y, which is x-8. Substituting [tex]y=x-8[/tex] into the first equation of the system of equation gives us:
[tex]2x+3y=1[/tex]
[tex]2x+3(x-8)=1[/tex]
Use the distributive property to help simplify and solve for x
[tex]2x+3x-24=1[/tex]
Combine like terms
[tex]5x-24=1[/tex]
Add 24 to both sides
[tex]5x-24+24=1+24[/tex]
[tex]5x=25[/tex]
Finally, divide both sides by 5
[tex]x=5[/tex]
Now, let's use [tex]x=5[/tex] in the equation [tex]y=x-8[/tex] to find the value of y
[tex]y=x-8[/tex]
[tex]y=5-8[/tex]
[tex]y=-3[/tex]
Now, we have the values x=5 and y=-3. Putting these values into an ordered pair gives us the answer (5,-3), which is the last answer choice.
Let me know if you need any clarifications, thanks!
~ Padoru