How do you solve $x + y/3 = 4$ and $x/4 - y = 6$ ?

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Answer 1 · 2015-07-17T09:04:24

$x=72/13,y=-60/13$

Step 1: Make $y$ the subject of one of the equations:
$x+y/3=4$ => $y=12-3x$

Step 2: Substitute this into the other equation and solve for $x$ :
$x/4-y=x/4-12+3x=6$ => $x-48+12x=24$
=> $x=72/13$

Step 3: Use this value in one of the equations and solve for $y$ :
$x+y/3=72/13+y/3=4$ => $y/3=52/13-72/13=-20/13$
=> $y=-60/13$

How do you solve x + y/3 = 4x + y/3 = 4 and x/4 - y = 6x/4 - y = 6?