Question

How can one fifth x − 2 = one third x + 8 be set up as a system of equations?

Answer options:
a. 5y − 5x = −10
3y − 3x = 24

b. 5y − 5x = −10
3y + 3x = 24

c. 5y + x = −10
3y + x = 24

d. 5y − x = −10
3y − x = 24

Thanks in advance!

Answer 1

\(\bf \cfrac{1}{5}x-2=\cfrac{1}{3}x+8?\)

Answer 2

@jdoe0001 correct.

Answer 3

this can be solved without using 'simultaneous equations' since there is only one variable x.

However you can take each side of the equation and set up as a separate equation

y= x/5 -2
y= x/3 +8

Just rearrange THOSE equations until they give you one of the answers

Answer 4

\(\large {
\begin{array}{cccllll}
\cfrac{1}{5}x-2&=&\cfrac{1}{3}x+8\\
y&=&y
\\\hline\\
y=\cfrac{1}{5}x-2&&y=\cfrac{1}{3}x+8
\end{array}\implies
\begin{cases}
y=\cfrac{1}{5}x-2\\
y=\cfrac{1}{3}x+8
\end{cases}
}\)

as MrNood indicated

Answer 5

now, neither of those look like any of the choices

but you can simplify them some by

1st one -- multiply both sides by 5
2nd one -- multiply both sides by 3

Answer 6

try doing what @jdoe0001 suggested above

multiply those equaitons and the answer will be clear

Answer 7

y= x/5 -2 multiply this by 5 both sides
y= x/3 +8 multiply this by 3 both sides

Answer 8

This is not an efficient way to solve for x,

x − 2 = 1/3 (x + 8)

treat each side as separate functions
y= x/5 - 2
y= x/3 +8

now clear the fractions

Answer 9

This is exactly as 2 people have posted above

and btw:
you have a typo it's x/5-2 = x/3 + 8 as confirmed by OP

your brackets are in the wrong place on right hand side.

As noted above there is only one variable so this can be solved without simultaneous equations

Answer 10

@LelandP

Answer 11

@Isherron @LelandP No need for other shout outs - the answer is clearly give by no less than THREE competent people above

Just DO the multiplication - the answer is there...