Question

the equation of line S is y=1 / 3 x - 3 The equation of the line T is y=-x+5The solution to the system of equation is located at Point p. which graph correctly show line S line T amd point P

Answer 1

To find the point of intersection we have to solve the system:

$\begin{gathered} y=\frac{1}{3}x-3 \\ y=-x+5 \end{gathered}$

Since, both equations are solve for y, we equate them to find x:

$\begin{gathered} \frac{1}{3}x-3=-x+5 \\ \frac{1}{3}x+x=5+3 \\ \frac{4}{3}x=8 \\ x=8(\frac{3}{4}) \\ x=\frac{24}{4} \\ x=6 \end{gathered}$

Now, we find the value of y by plugging the value of x in one of the equations:

$y=-6+5=-1$

Therefore, the point of intersection is (6,-1). Then, the answer is C.