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Answered

How can 1/2x - 5 = 1/3x + 6 be set up as a system of equations?


A: 2y+x = -10

3y+x = 18


B: 2y+2x = -10

3y+3x = 18


C: 2y-x = -10

3y-x=18


D: 2y-2x = -10

3y-3x= 18

Verified Answer :

y = 1/2x - 5...2y = x - 10...2y - x = -10
y = 1/3x + 6....3y = x + 18...3y - x = 18
answer C

Answer:

\(2y - x = -10\)

\(3y-x=18\)

Step-by-step explanation:

Set up as a system of equation

\(\frac{1}{2} x - 5 = \frac{1}{3} x + 6\)

To get system of equations, we set each side of the given equation equals to y

\(\frac{1}{2} x - 5=y\)

Multiply whole equation by 2. That is we multiply each term by 2

\(x - 10=2y\)

Subtract x on both sides

\(2y - x = -10\) (first equation)

\(y = \frac{1}{3} x + 6\)

Multiply whole equaiton by 3

\(3y=x +18\)

Subtract x on both sides

\(3y-x=18\) (second equation)