If (p, q) is the solution to the system of equations, what is the value of q? −16p − 2q = 100
p − 4q = 200

The solution to the system of equations

Hence, the value of q = -50

Step-by-step explanation:

Given the system of equations

solving to determine the value of q

Multiply p − 4q = 200 by 16:      

so adding the equations

so

solve -66q = 3300

Divide both sides by -66

substituting q = -50 in −16p − 2q = 100

Subtract 100 from both sides

Simplify

Divide both sides by -16

Thus, the solution to the system of equations

Hence, the value of q = -50

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.