Define system of linear equations. When a system of equations is consistent? Make echelon form to solve: -2a - 3b + 4c = 5 b - 2c = 4 a + 3b - c = 2

System of 3 equations in 3 unknowns: $$-2a - 3b + 4c = 5 \quad \cdots (1)$$ $$b - 2c = 4 \quad \cdots (2)$$ $$a + 3b - c = 2 \quad \cdots (3)$$ --- A linear equation in $n$ variables has the form: $$a1x1 + a2x2 + \cdots + anxn = b$$ where $a1, a2, \ldots, an$ and $b$ are constants and