How do you solve this system of equations: #2x + 3y \geq 6;x - y \leq 3#?

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Answer 1 · 2018-02-26T23:24:34

See below.

To avoid the inequality we equate

#{(2 x + 3 y = 6 + epsilon_1^2),(x - y = 3 - epsilon_2^2):}#

with #{epsilon_1,epsilon_2} in RR #

Now solving for #x,y#

#{(x = 3+1/5 epsilon_1^2-3/5epsilon_2^2),(y = 1/5(epsilon_1^2+epsilon_2 ^2)):}#

and we conclude that #y ge 0# but for #x# the result is inconclusive. Depends on #epsilon_1,epsilon_2#

Any way, the solution set is the union for #{epsilon_1, epsilon_2} in RR#

of

#{(x = 3+1/5 epsilon_1^2-3/5epsilon_2^2),(y = 1/5(epsilon_1^2+epsilon_2 ^2)):}#