Chapter 10 - Section 10.5 - Equations of Lines - Exercises - Page 472: 48

$C=7$

Since the three lines are concurrent, the three lines all intersect at one point. We can rearrange the equation of the second line: $2x+y = 5$ $y = 5-2x$ We can replace $y$ in the third equation to find the x-coordinate: $x-y=4$ $x-(5-2x) = 4$ $x-5+2x=4$ $3x = 9$ $x = 3$ We can find the y-coordinate: $y = 5-2x$ $y = 5-2(3)$ $y = 5-6$ $y = -1$ We can find the value of $C$: $3x+2y=C$ $C = 3(3)+2(-1)$ $C = 9-2$ $C=7$