The lines -2x + y =k and 0.5x +y = 14 intersect when x= -8.4. What is the value of k?
+133 The two lines intersect when the y's and x's are equal. Thus, we can convert each to slope-intercept form:
\(y=2x+k, y=-0.5x+14\)
Thus, the lines intersect when \(2x+k = -0.5x+14 \text{ or } 2.5x=14-k\).
Consequently, k = 14-2.5*-8.4 = 35.
