\#2A Find the area of the shaded region below. \[ -x+2 \] \[ 16 x-12 \] Partner A's answer Partner B's answer

Step 1 ：Find the intersection points of the lines $y=-x+2$ and $y=16x-12$ by solving the equation $-x+2=16x-12$

Step 2 ：Calculate the value of x: $x=\frac{10}{17}$

Step 3 ：Substitute the value of x back into $y=-x+2$ to find the value of y: $y=\frac{24}{17}$

Step 4 ：The vertices of the triangle are $(0,2)$, $(0,-12)$, and $(\frac{10}{17},\frac{24}{17})$

Step 5 ：Take the side joining $(0,2)$ and $(0,-12)$ as the base of the triangle

Step 6 ：Calculate the area of the triangle: $\frac{1}{2}(\text{base})(\text{height})=\frac{1}{2}(2-(-12))(\frac{10}{17})$

Step 7 ：Simplify the area: $\frac{1}{2}(14)(\frac{10}{17})=\boxed{\frac{70}{17}}$ square units