Question

Solve using substition 2x+y=-16 -7x+9y=6

Answer 1

Solve the following system using substitution:
{2 x + y = -16
{9 y - 7 x = 6

In the first equation, look to solve for y:
{2 x + y = -16
{9 y - 7 x = 6

Subtract 2 x from both sides:
{y = -2 x - 16
{9 y - 7 x = 6

Substitute y = -2 x - 16 into the second equation:
{y = -2 x - 16
{9 (-2 x - 16) - 7 x = 6

9 (-2 x - 16) - 7 x = (-18 x - 144) - 7 x = -25 x - 144:
{y = -2 x - 16
{-25 x - 144 = 6

In the second equation, look to solve for x:
{y = -2 x - 16
{-25 x - 144 = 6

Add 144 to both sides:
{y = -2 x - 16
{-25 x = 150

Divide both sides by -25:
{y = -2 x - 16
{x = -6

Substitute x = -6 into the first equation:
{y = -4
{x = -6
Collect results in alphabetical order:
Answer:  {x = -6 , y = -4