Answer:
{p, q, r} = {2, 5, -1}
Step-by-step explanation:
p + q + 3r = 4 ....equation(i)
2q + 3r = 7 ......equation(ii)
p - q - r = -2 .......equation(iii)
Solve equation (iii) in terms of p:
p - q - r = -2
p = q + r - 2
putting this equation in (i) at the place of p:
(q + r - 2) + q + 3r = 4
q + q + r + 3r = 4 + 2
2q + 4r = 6 .......(iv)
solve the equation (ii) in terms of r :
2q + 3r = 7
3r = 7 - 2q
r = \frac{7}{3} - \frac{2q}{3}
putting the value of r in equation (iv) :
2q + 4(\frac{7}{3} - \frac{2q}{3}) = 6
- \frac{2q}{3} = - \frac{10}{3}
-2q = - 10
q = \frac{10}{2}
q = 5
Now,
r = \frac{7}{3} - \frac{2q}{3}
use th value of q to find the value of r :
r = \frac{7}{3} - \frac{2q}{3} * 5
r = -1
Then, use the value of q and r to find the value of p:
p = 5 + (-1) -2
p = 2
