Solve the following system:
{4 y - 5 x = -7
-16 y + 17 x = 31
In the first equation, look to solve for x:
{4 y - 5 x = -7
-16 y + 17 x = 31
Subtract 4 y from both sides:
{-5 x = -4 y - 7
-16 y + 17 x = 31
Divide both sides by -5:
{x = (4 y)/5 + 7/5
-16 y + 17 x = 31
Substitute x = (4 y)/5 + 7/5 into the second equation:
{x = (4 y)/5 + 7/5
17 ((4 y)/5 + 7/5) - 16 y = 31
17 ((4 y)/5 + 7/5) - 16 y = ((68 y)/5 + 119/5) - 16 y = -(12 y)/5 + 119/5:
{x = (4 y)/5 + 7/5
(-(12 y)/5 + 119/5) = 31
In the second equation, look to solve for y:
{x = (4 y)/5 + 7/5
-(12 y)/5 + 119/5 = 31
Subtract 119/5 from both sides:
{x = (4 y)/5 + 7/5
-(12 y)/5 = 36/5
Multiply both sides by -5/12:
{x = (4 y)/5 + 7/5
y = -3
Substitute y = -3 into the first equation:
Answer: x = -1 y = -3