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

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hysgubwyri3 · Accepted Answer

Step 1  To find the solution of inequalities:  y≤5−3x (1)  y+19≥x−8x⇒y+19≥−7x  ⇒y≥−7x−19 (2)  Step 2  Multiply equation (ii) by (-1) and reverse the direction of the inequality symbol:  y≥−7x−19  (−1)y≤(−1)(−7x−19)  −y≤7x+19 (3)  Step 3  Adding equation (i) and (iii):  Adding (y≤5−3x) and (−y≤7x+19):  −y+y≤5−3x+7x+19  0≤4x+24  4x+24≥0  Step 4  Use the additive property of inequalities, the same amount is added to both sides of the inequality. Add (-24) to each side of the equation.  4x+24≥0  4x+24+(−24)≥(−24)  4x≥(−24)  x≥−244  x≥−6  Step 5  Put the value of x in equation (i):  y≥−7x−19 and x≥−6:  y≥−7(−6)−19  y≥42−19  y≥23  Step 6  Hence, the solution of inequalities:  f(x,y)={(x,y)∈R2∣x≥−6,y≥23}

Donald Cheek · Accepted Answer

Step 1  Given the system of inequalies  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≤8 to obtain the inequality for y as,  −y+53≤8 and −y+53≥−3  −y≤19 and −y≥−14⇒y≤14  Thus, −19≤y≤14

nick1337 · Accepted Answer

We have, y≤5−3x (1) y+19≥x−8x ⇒y+19≥−7x ⇒−y−19≤7x (2) [Multiplying by -1] Adding (1) and (2), we get, y−y−19≤5−3x+7x ⇒−19≤5+4x ⇒−24≤4x ⇒4x≥−24 ⇒x≥−6 Putting the value of x in (1), we get y≤5−3x(−6) ⇒y≤5+18 ⇒y≤23 Hence, x≥−6 and y≤23

Using algebra,find the solution to the system of inequalities below

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