Using algebra, find the solution to the system of inequalities below y≤5−3x y+19≥x2−8x

Question

Using algebra, find the solution to the system of inequalities below  y≤5−3x  y+19≥x2−8x

Jonathan Burroughs · Accepted Answer

Step 1  Given, y≤5−3x,y+19≥x2−8x  Step 2  y+19−19≥x2−8x−19 [Subtract by 19]  y≥x2−8x−19  x2−8x−19≤y  So, x2−8x−19≤y≤5−3x  x2−8x−19−5+3x≤5−3x−5+3x [Subtract 5 and add 3x]  x2−8x+3x−24≤0  x(x−8)+3(x−8)≤0  (x+3)(x−8)≤0  Step 3  The region is possible when (x+3)≥0,(x−8)≤0⇒x≥−3 and x≤8  So, −3≤x≤8. In interval notation, x∈[−3,8]  Step 4  Now, (−3)(−3)≥−3x≥(−3)8 [Multiply by -3]  9≥−3x≥−24  −24≤−3x≤9  5−24≤5−3x≤5+9 [Add 5]  −19≤y≤14  In interval notation, y∈[−19,14]  Step 5  Hence, the solution of system of inequalities is x∈[−3,8],y∈[−19,14].

Becky Harrison · Accepted Answer

Step 1  Given: y≤5−3x (1)  y+19≥x−8x (2)  Step 2  Simplify the equation (2)  y+19≥x−8x  y+19≥−7x  y≥−7x−19  y≥−(7x+19)  −y≤7x+19 (3)  Step 3  Add equation (1) and (3)  0≤4x+24  −24≤4x  4x≥−24  x≥−6  Step 4  Put the value of x in equation (3)  −y≤7(−6)+19  −y≤−23  y≥23  Step 5  Answer: {(x,y)∈R2∣x≥−6,y≥23}

nick1337 · Accepted Answer

Step 1 Given the system of inequalities y≤5−3x y+19≥x2−8x Simplify the inequality y+19≥x2−8x as, y+19≥x2−8x y≥x2−8x−19 x2−8x−19≤5−3x x2−8x−19+3x≤5−3x+3x x2−5x−19≤5 x2−5x−24≤0 (x+3)(x−8)≤0 −3≤x≤8 Step 2 Simplify the inequality y≤5−3x as, y≤5−3x 5−3x≥y −3x≥y−5 x≤−y+53 Thus, −3≤x≤8 Since −3≤x≤8obtain the inequality for y as, −y+53≤8 and −y+53≥−3 −y≤19 and −y≥−14⇒y≤14 Thus,−19≤y≤14 Therefore, the solution is −3≤x≤8 and −19≤y≤14

Using algebra, find the solution to the system of inequalities

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