Question

How can (1/6)x − 5 = (1/5)x + 2 be set up as a system of equations? (6 points)

Answer 1

hello :
a system of equations is :
y = (1/6)x − 5
y = (1/5)x + 2

Answer 2

Hey there!

You could represent this as a system of equations by solving each side of the equation as its own individual equation. You would do this by taking each side of the equation and setting it equal to y, then simplifying.

1/6x – 5 = y

You could then choose to make 1/6x into 1x and multiply the entire equation by 6 to express it a little easier.

(1/6x – 5 = y)(6)
x – 30 = 6y

Now, just get x and y on the same side of the equation.

x – 30 = 6y
+ 30 + 30

x = 6y + 30
–6y –6y

x – 6y = 30

Just repeat this with the other equation

(1/5x + 2 = y)(5)
x + 10 = 5y

x + 10 = 5y
– 10 –10

x = –10 + 5y
– 5y – 5y

x – 5y = –10

So, your final system of equations is:

x – 6y = 30
x – 5y = –10

Hope this helped you out! :-)