Answer:
{c = 25/4
{t = 6
{x = 1
Step-by-step explanation:
Solve the following system:
{2 (x - 6) + 5 = -5 | (equation 1)
{75 = 3 (3 t - 2) + 27 | (equation 2)
{x - 2/3 (6 c - 9) = -18 | (equation 3)
Express the system in standard form:
{0 c+0 t+2 x = 2 | (equation 1)
{0 c - 9 t+0 x = -54 | (equation 2)
{-(4 c) + 0 t+x = -24 | (equation 3)
Swap equation 1 with equation 3:
{-(4 c) + 0 t+x = -24 | (equation 1)
{0 c - 9 t+0 x = -54 | (equation 2)
0 c+0 t+2 x = 2 | (equation 3)
Divide equation 2 by -9:
{-(4 c) + 0 t+x = -24 | (equation 1)
{0 c+t+0 x = 6 | (equation 2)
{0 c+0 t+2 x = 2 | (equation 3)
Divide equation 3 by 2:
{-(4 c) + 0 t+x = -24 | (equation 1)
{0 c+t+0 x = 6 | (equation 2)
{0 c+0 t+x = 1 | (equation 3)
Subtract equation 3 from equation 1:
{-(4 c)+0 t+0 x = -25 | (equation 1)
{0 c+t+0 x = 6 | (equation 2)
{0 c+0 t+x = 1 | (equation 3)
Divide equation 1 by -4:
{c+0 t+0 x = 25/4 | (equation 1)
{0 c+t+0 x = 6 | (equation 2)
{0 c+0 t+x = 1 | (equation 3)
Collect results:
Answer: {c = 25/4
{t = 6
{x = 1
