Question

Which of the following equations is non-linear?

x = 8x + 19 - 10y
2x + 13y + 14x - 7 = 16y - 3
x + 12 = -8x + 10 - 2y
2x + 6y = 14y - 19x 2 + 12

Answer 1

A linear equation in x and y has each variable to the first power and no products of variables. Simplifying each:

1) x = 8x + 19 − 10y → 7x − 10y + 19 = 0 (linear)
2) 2x + 13y + 14x − 7 = 16y − 3 → 16x − 3y − 4 = 0 (linear)
3) x + 12 = −8x + 10 − 2y → 9x + 2y + 2 = 0 (linear)
4) 2x + 6y = 14y − 19x^2 + 12 → 19x^2 + 2x − 8y − 12 = 0 (non-linear because of x^2)

Therefore the fourth equation is non-linear.