Question

2x - 3y = -1 y = x - 1 Solve for both x and y using elimination.

Answer 1

Solve the following system using elimination:
{2 x - 3 y = -1 | (equation 1)
{y = x - 1 | (equation 2)

Express the system in standard form:
{2 x - 3 y = -1 | (equation 1)
{-x + y = -1 | (equation 2)

Add 1/2 × (equation 1) to equation 2:
{2 x - 3 y = -1 | (equation 1)
{0 x - y/2 = (-3)/2 | (equation 2)

Multiply equation 2 by -2:
{2 x - 3 y = -1 | (equation 1)
{0 x+y = 3 | (equation 2)

Add 3 × (equation 2) to equation 1:
{2 x+0 y = 8 | (equation 1)
{0 x+y = 3 | (equation 2)

Divide equation 1 by 2:
{x+0 y = 4 | (equation 1)
{0 x+y = 3 | (equation 2)
Collect results:
Answer:  {x = 4, y = 3