Solve the following system:
{3 y-3 x = -3 | (equation 1)
9 x-12 y = -18 | (equation 2)
Swap equation 1 with equation 2:
{9 x-12 y = -18 | (equation 1)
-(3 x)+3 y = -3 | (equation 2)
Add 1/3 × (equation 1) to equation 2:
{9 x-12 y = -18 | (equation 1)
0 x-y = -9 | (equation 2)
Divide equation 1 by 3:
{3 x-4 y = -6 | (equation 1)
0 x-y = -9 | (equation 2)
Multiply equation 2 by -1:
{3 x-4 y = -6 | (equation 1)
0 x+y = 9 | (equation 2)
Add 4 × (equation 2) to equation 1:
{3 x+0 y = 30 | (equation 1)
0 x+y = 9 | (equation 2)
Divide equation 1 by 3:
{x+0 y = 10 | (equation 1)
0 x+y = 9 | (equation 2)
Collect results:
Answer: | x = 10 and y=9
+130517 -3x+3y=-3 divide everything by -3 → x - y = 1 add y to both sides → x = 1 + y (1)
9x-12y=-18 (2)
Subbing (1) into (2), we have
9(1 + y) - 12y = - 18 simplify
9 + 9y - 12y = -18
9 - 3y = -18 subtract 9 from both sides
-3y = -27 divide both sides by -3
y = 9
And using (1) ..... x = 1 + y = 1 + 9 = 10
