Solve the system of inequalities graphically:x− 2y≤3,3x+4y≥12,x≥0,y≥1

Question

Solve the system of inequalities graphically:x− 2y≤3,3x+4y≥12,x≥0,y≥1

Filo · Accepted Answer

First we solve x−2y≤3Lets first draw graph of x−2y=3Putting x=0 in (1)0−2y=3−2y=3y=−23​y=−1.5Putting y=0 in (1)x−2(0)=3x−0=3x=3Refer image 1.xy​0−1.5​30​Points to be plotted are (0,6),(3,0)Checking for (0,0)Putting x=0, y=0x−2y≤30−2(0)≤30≤3Which is true Hence origin lies in plane x−2y≤3So, we shade left of lineNow we solve 3x+4y≥12Lets first draw graph of3x+4y=12Putting x=0 in (1)3(0)+4y=120+4y=124y=12y=412​y=3Putting y=0 in (1)3x+4(0)=123x+0=123x=12x=312​x=4Refer image 2.xy​03​40​Points to be plotted are (0,3),(4,0)checking for (0,0)Putting x=0,y=03+4y≥123(0)+2(0)≥120≥12which is falseHence origin does not lie in plane 3x+2y>6So, we shade rights side of line.Also y≥1So, for all values xRefer image 3.x0−14y111Points to be plotted are (0,1),(−1,1),(4,1)Also x≥0So, the shaded region will lie on the right side of y-axisHence the shaded region represents the given inequality.

Question Text	Solve the system of inequalities graphically: $x - 2 y \leq 3, 3 x + 4 y \geq 12, x \geq 0, y \geq 1$
Answer Type	Text solution:1
Upvotes	150

Solve the system of inequalities graphically:
$x - 2 y \leq 3, 3 x + 4 y \geq 12, x \geq 0, y \geq 1$

Text solutionVerified

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