Question

4,5,6

pendent express solutions in terms of the parameter YYPP999 Solve the system of equations. If the system is dependent, express 4) x+y+ .7 x-y + 4 .9 5x + y = -19 Solve the problem by writing and solving a suitable system of equations 5) IF 10 pounds of sugar and 40 pounds of flour cost $29 and 30 pounds of sugar and 20 pounds of flour cost $27, what is the price per pound of sugar and flour? Graph the feasible region for the system of inequalities. 6) x + 2y > 2 *yo # H

Answer 1

4)

In matrir form,

5 11/ —19/

Using gauss elimination method,

Rewrite the system in matrix form and solve it by Gaussian Elimination (Gauss-Jordan elimination) | 1 1 1 -7 |1 -1 4 -9 15 1 1 -19 R2-1 R1 R2 (multiply 1 row by 1 and subtract it from 2 row); R3 - 5 R1 R3 (multiply 1 row by 5 and subtract it from 3 row) | 1 1 1 |-7) 10 -4 -4 16 R2/-2 → R2 (divide the 2 row by -2) | 1 1 1 -7 101 -1.5 1 To -4 -4 16 ) R1-1 R2 → R1 (multiply 2 row by 1 and subtract it from 1 row); R3 +4 R2 R3 (multiply 2 row by 4 and add it to 3 row) | 102.5 -8 101 -1.5 1 TOO -10 20 R3/-10 → R3 (divide the 3 row by -10) | 1 0 2.5 -8 0 1 -1. 51 100 1 -2

R1 - 2.5 R3 → R1 (multiply 3 row by 2.5 and subtract it from 1 row); R2 +1.5 R3 → R2 (multiply 3 row by 1.5 and add it to 2 row) | 1 0 0 -3

Thus,

(x,y,z)=(-3,-2,-2)

5)

Let x1= Cost price of Sugar

x2= Cost price of Flour

Thus, the system of equations, we get,

10x1 + 40x2 = 29 30Xų + 2022 = 27 Rewrite the system in matrix form and solve it by Gaussian Elimination (Gauss-Jordan elimination) 10 40 29 | 30 20 | 27 R1 / 10 → Ri (divide the 1 row by 10) | 14 | 2.9 | | 30 20 | 27 | R2-30 R1 R2 (multiply 1 row by 30 and subtract it from 2 row) R2/-100 — R2 (divide the 2 row by -100) R1 - 4 R2 → R1 (multiply 2 row by 4 and subtract it from 1 row) 2 = 0.5 x2 = 0.6

6) Overlapping region is feasible region

x + 2y > 2 x - y< 0

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