Find the value of a so that the system
y=11x+14
2y−4=ax-y+5x+6
has no solutions.
Add y to both sides in the second equation. This yields us \(3y - 4 = ax + 5x + 6 \)
Because we have 3 y's, the slope of this equation (coefficient of x) must be 3 times the coefficient of x in the first equation.
This means we have the equation: \(ax + 5x = 33x\), meaning \(a = \color{brown}\boxed{28}\)