At what point does a line with a slope of 34 and a y-intercept of -5 intersect a line with a slope of −14 and a y-intercept of 3?

Set them into slope-intercept forms of equations then set those equations equal to each other and solve for x and y.  y = 34x - 5 and y = -14x+3.  Set those equal to each other, solve for x to get x = 1/6.  Sub in that x value to get y = 2/3.  The point where they intersect is the solution of the system; in other words, where on both lines we have the exact same (x, y) value.