For what values of k does the line y = kx –4 pass through the point of intersection of the lines y=2x–5 and y=–x+1?

First, we want to find the point of intersection of y=2x-5 and y= -x+1 by solving a system of equations. we can use the substitution method, since both equations are already solved for y: 2x-5=-x+13x=6x=2now we can plug in this x value to one of the original equations to find the y value: y=(-2)+1y=-1therefore, our point of intersection is (2,-1). we can now plug this into the equation y=kx-4 to solve for k because we know that the line must pass through this point: -1=k(2)-43=k(2)k=2/3

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