hi can someone please help with homework please

Question

Question 1: Classify the system of equations and identify the number of solutions.

35x + 5y = 15

y = 3 − 7x

A.) consistent, independent; one

B.) consistent, dependent; one

C.) inconsistent; none

D.) consistent, dependent; infinite

Question 2: Minimize the objective function P = 45x + 48y for the given constraints.

x ≥ 0

y ≥ 0

5x + y ≥ 16

x + 3y ≥ 6

A.) 768

B.) 84

C.) 183

D.) 270

hello can please explain and solve.

Answer 1

1) D. Consistent, dependent, infinite solutions. If you graphed the two lines, they'd be the same line

multiply the 2nd equation by 5 and you get the 1st equation. They are equivalent equations, linearly

dependent. an infinite number of (x,y) points would satisfy the equations. such as (1,-4), (0, 3)

(-1, 10), (2, -11), ....and endless other points

2) C. 183. check 3 points, (6,0) P= 270, (0,16) P=768, (3,1) P = 183

those points are the lower bound intersections of the constraints

45(3)+48(1) = 135+48 = 183