Question

Solve the following system by the comparison method.

2p + q = 1
9p + 3q + 3 = 0

What is the solution set?

{(-2, 5)}
{(2, -5)}
{(-2, -5)}

Answer 1

2p + q = 1
9p + 3q + 3 = 0

q = 1 - 2p
replace q = 1 - 2p into 9p + 3q + 3 = 0

9p + 3(1 - 2p) + 3 = 0
9p + 3 - 6p + 3 = 0
3p + 6 =0
3p = -6
p = -2

q = 1 - 2p
q = 1 -2(-2)
q = 1 + 4
q = 5

(-2 , 5)

answer
{(-2, 5)} first one

Answer 2

Solution set is {-2,5}

First option is correct!

Explanation:

2p+q = 1 ,solving the equation for q

q = 1-2p ..... equation (1)

9p+3q+3=0,dividing the equation by 3

3p+q+1=0, using substituting method

3p+(1-2p)+1=0

3p-2p+2 =0

p +2 =0

p=-2

substituting the value of p in q=1-2p ,we get

q = 1-2(-2) = 1+4 =5

solving it for p and q ,we get (-2,5) solution set is {(-2,5)}