How do you solve the system of inequalities $3x-4y<=12$ and $-2x+5y>=10$ ?

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Answer 1 · 2018-07-16T12:05:51

$y>=min(2+2/5x,-3+3/4x)$

Solving the first inequality for $y$

subtracting $3x$ we get

$-4y<=12-3x$

dividing by $-4$

$y>=-3+3/4x$
solving the second inequality for $y$

adding $2x$

$5y>= 10+2x$

dividing by $5$

$y>=2+2/5x$
so

$y>=2+2/5x$

and

$y>=min(2+2/5x,-3+3/4x)$

How do you solve the system of inequalities 3x-4y<=123x-4y<=12 and -2x+5y>=10-2x+5y>=10?