Question

(06.03)

How can one half x − 5 = one third x + 6 be set up as a system of equations? (6 points)

Answer 1

yes it can

Explanation:

1/2x-5=1/3x+6

Answer 2

Answer: third option.

Explanation:

`(1)/(2)x-5=(1)/(3)x+6` can be rewritten into two separate equationts:

`\left \{ {{ y=(1)/(2)x-5} \atop {y=(1)/(3)x+6}} \right.\\\\`

You can observe that this linear equations are written in Slope-Intercept form:

`y=mx+b`

But the equations shown in options provided are written in Standard form:

`Ax+By=C`

Therefore, you need to move the x term to the left side of the equation (In each equation):

- For the first equation:

`y-(1)/(2)x=-5`

Simplifying:

`(2y-x)/(2)=-5\\\\2y-x=-10`

- For the second equation:

`y-(1)/(3)x=6`

Simplifying:

`(3y-x)/(3)=6\\\\3y-x=18`

Then the system of equations is:

`\left \{ {{2y-x=-10} \atop {3y-x=18}} \right.`