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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

Respuesta :

texaschic101
y = 1/2x - 5...2y = x - 10...2y - x = -10
y = 1/3x + 6....3y = x + 18...3y - x = 18
answer C

Answer:

[tex]2y - x = -10[/tex]

[tex]3y-x=18[/tex]

Step-by-step explanation:

Set up as a system of equation

[tex]\frac{1}{2} x - 5 = \frac{1}{3} x + 6[/tex]

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

[tex]\frac{1}{2} x - 5=y[/tex]

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

[tex]x - 10=2y[/tex]

Subtract x on both sides

[tex]2y - x = -10[/tex] (first equation)

[tex]y = \frac{1}{3} x + 6[/tex]

Multiply whole equaiton by 3

[tex]3y=x +18[/tex]

Subtract x on both sides

[tex]3y-x=18[/tex] (second equation)

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