The value of p for which the lines 3x + y + 2 = 0, 2x - y + 3 = 0, and x+
py = 3 are concurrent is

Step-by-step explanation:

the system is :  3x + y + 2 = 0.......(1)

                          2x - y + 3 = 0......(2)

                         x+ py - 3 = 0......(3)

(1)+(2) : 3x+y+2 +2x-y+3 =0

           5x+5 =0

so : x = -1

put x = -1 in equation (2) : 2(-1)-y+3 = 0

so : y = 1

the intersection point is A(-1 ; 1)

put x = -1 and y = 1 in equation (3) : -1+p(1)-3 =0        so : p = 4

sketch the line :3x + y + 2 = 0 and 2x - y + 3 = 0 and  x+ 4y - 3 = 0

y = -3x-2 ...(color red)  and y=2x+3....(color blue) and  y = -1/4x +3/4...(color purple)

step-by-step explanation:

y = 2x

step-by-step explanation:

if you divide each number in the sequence, you'll see that they all have a multiple factor of 2. each number in the series, and any other numbers which may continue, will be multiplied by 2. therefore, y is the next number in the sequence, and x is the current one, so, our formula will be y = 2x.