Create a system of equations that has a solution of (3, -1)

y = x  -4

y = 2x - 7

(answers may differ depending on slope chosen, see below)

Step-by-step explanation:

use the point-slope form for a linear equation, which is

(y-y₁) = m(x-x₁)

recall m = slope and (x₁,y₁) are simply any point on the line

in our case, since both equations have (3,-1) as solutions, that means both lines intersect at (3,-1) which also means that for both equations, x₁=3 and y₁=-1

hence the equation becomes

(y-(-1) ) = m(x-3)

(y+1) = m(x-3)

y+1 = m(x-3)

in order to express the above equation as 2 different equations with the same   (x₁,y₁), all we need to do is to choose 2 random values for m

we'll pick m = 1 and m = 2 which gives us our 2 equations

y+1 = x-3 (rearranging)

y = x -4

and

y+1 = 2(x-3) (rearrange)

y = 2x - 7

answer: evaluate the objective function at each vertex to determine which - and -values, if any, maximize or minimize the function. example: find the minimum value and maximum value of the objective function f ( x , y ) = 4 x + 5 y , subject to the following constraints

step-by-step explanation:

abc