Which value of k would cause the system of linear equations 35x+14y=119 and 5x+2y=k to have an infinite number of solutions?

The 2 equations are lines on an x/y plane.  They are going to have an infinite number of solutions if those lines lie on top of each other.  so the first thing you need to do is to get 5x+2y to look like 35x+14y.  To do this we need to multiply both sides of the equation by 7 so 5x+2y=k becomes 35x+14y=7k. Now that the left hand side of both equations are the same we can set the right hand side of the equations equal to each other 119=7k or k = 17.  Hope that helps.