Question

Solve for p and q simultaneously if: $\left \{ {{6q+7p=3} \atop {2q+p=5}} \right.$

Answer 1

6q + 7p = 3
2q + p = 5      

 first step: make both first terms equal by multiplying second equation by3    2q(3) + p(3) = 5(3)
  6p + 3p = 15
      
second step: subtract second equation from first equation
 (6p + 7p = 3)  -
 (6p + 3p = 15)
so you get :  
 4p = -12
 p = -12/4
 p = -3   (value of p)

third step: now use the value of p to find q
6q + 7(-3) = 3
6q - 21 = 3
6p = 3 + 21
q = 24 / 6
q = 4

so p = -3 and q = 4