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

Answer:

yes it can

Step-by-step explanation:

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

Answer 2

Answer: third option.

Step-by-step explanation:

$\frac{1}{2}x-5=\frac{1}{3}x+6$ can be rewritten into two separate equationts:

$\left \{ {{ y=\frac{1}{2}x-5} \atop {y=\frac{1}{3}x+6}} \right.$

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:

$y-\frac{1}{2}x=-5$

Simplifying:

$\frac{2y-x}{2}=-5\\\\2y-x=-10$

 - For the second equation:

$y-\frac{1}{3}x=6$

Simplifying:

$\frac{3y-x}{3}=6\\\\3y-x=18$

Then the system of equations is:

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