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Solve 2x−y>52x - y > 5 and x+3y<10x + 3y < 10 for (x,y)(x, y)

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Full solution

Q. Solve 2x−y>52x - y > 5 and x+3y<10x + 3y < 10 for (x,y)(x, y)
  1. Identify Inequalities: Identify the inequalities to solve:\newlineWe have two inequalities:\newline11. 2x−y>52x - y > 5\newline22. x+3y<10x + 3y < 10
  2. Isolate yy - 11st Inequality: Isolate yy in the first inequality:\newlineAdd yy to both sides of 2x−y>52x - y > 5:\newline2x>y+52x > y + 5\newlineNow, subtract 55 from both sides:\newline2x−5>y2x - 5 > y\newlineSo, y<2x−5y < 2x - 5
  3. Isolate yy - 22nd Inequality: Isolate yy in the second inequality:\newlineSubtract xx from both sides of x+3y<10x + 3y < 10:\newline3y<10−x3y < 10 - x\newlineNow, divide all terms by 33:\newliney<10−x3y < \frac{10 - x}{3}
  4. Graph Solution Region: Graph the inequalities to find the solution region:\newlineWe need to graph y<2x−5y < 2x - 5 and y<10−x3y < \frac{10 - x}{3}.\newlineThe solution region will be the area where both conditions are satisfied on a coordinate plane.

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