How do you write $\frac{1}{2} x + \frac{1}{2} y = 6$ $1/2x+1/2y=6$ in standard form and what is A, B, C?

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How do you write $\frac{1}{2} x + \frac{1}{2} y = 6$ $1/2x+1/2y=6$ in standard form and what is A, B, C?

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Answer 1 · 2017-08-02T12:26:17

$1 x + 1 y = 12$ $1x+1y=12$

Explanation:

"standard form" for a linear equation is
$XXX A x + B y = C$ $color(white)("XXX")color(red)Ax+color(blue)By=color(magenta)C$
where
$XXX A, B, C$ $color(white)("XXX")color(red)A, color(blue)B, color(magenta)C$ are integers
$XXX$ $color(white)("XXX")$ (and usually with the restriction that $A \geq 0$ $color(red)A>=0$ )

Given
$XXX \frac{1}{2} x + \frac{1}{2} y = 6$ $color(white)("XXX")1/2x+1/2y=6$
Multiplying everything by $2$ $2$ converts the coefficients to integers:
$XXX 1 x + 1 y = 12$ $color(white)("XXX")color(red)1x+color(blue)1y=color(magenta)(12)$

Relating this back to the "standard form" we have
$XXX A = 1$ $color(white)("XXX")color(red)A=color(red)1$
$XXX B = 1$ $color(white)("XXX")color(blue)B=color(blue)1$ and
$XXX C = 12$ $color(white)("XXX")color(magenta)C=color(magenta)(12)$

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How do you write $\frac{1}{2} x + \frac{1}{2} y = 6$ $1/2x+1/2y=6$ in standard form and what is A, B, C?

1 Answer

Explanation:

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How do you write $\frac{1}{2} x + \frac{1}{2} y = 6$ $1/2x+1/2y=6$ in standard form and what is A, B, C?