Answer:
a = 65/18 , d = 1/2
Step-by-step explanation by elimination:
Solve the following system:
{9 a - 3 d = 31 | (equation 1)
-2 d = -1 | (equation 2)
Multiply equation 2 by -1:
{9 a - 3 d = 31 | (equation 1)
0 a+2 d = 1 | (equation 2)
Divide equation 2 by 2:
{9 a - 3 d = 31 | (equation 1)
0 a+d = 1/2 | (equation 2)
Add 3 × (equation 2) to equation 1:
{9 a+0 d = 65/2 | (equation 1)
0 a+d = 1/2 | (equation 2)
Divide equation 1 by 9:
{a+0 d = 65/18 | (equation 1)
0 a+d = 1/2 | (equation 2)
Collect results:
Answer: {a = 65/18 , d = 1/2