Answer:
{x = -3 , y = 10
Explanation:
Solve the following system:
{y = 9 - x/3 | (equation 1)
{y = (2 x)/3 + 12 | (equation 2)
Express the system in standard form:
{x/3 + y = 9 | (equation 1)
{-(2 x)/3 + y = 12 | (equation 2)
Swap equation 1 with equation 2:
{-(2 x)/3 + y = 12 | (equation 1)
{x/3 + y = 9 | (equation 2)
Add 1/2 × (equation 1) to equation 2:
{-(2 x)/3 + y = 12 | (equation 1)
{0 x+(3 y)/2 = 15 | (equation 2)
Multiply equation 1 by 3:
{-(2 x) + 3 y = 36 | (equation 1)
{0 x+(3 y)/2 = 15 | (equation 2)
Multiply equation 2 by 2/3:
{-(2 x) + 3 y = 36 | (equation 1)
{0 x+y = 10 | (equation 2)
Subtract 3 × (equation 2) from equation 1:
{-(2 x)+0 y = 6 | (equation 1)
{0 x+y = 10 | (equation 2)
Divide equation 1 by -2:
{x+0 y = -3 | (equation 1)
{0 x+y = 10 | (equation 2)
Collect results:
Answer: {x = -3 , y = 10