## Calculus: Early Transcendentals 8th Edition

$45 ^ \circ$
$2x-y=3$ $\implies$ $a=y=2x-3$ and $3x+y=7$ $\implies$ $b=y=-3x+7$ Thus, $a= \lt 1,2 \gt$ and $b = \lt 1,-3 \gt$ $\theta = cos^{-1}\dfrac{a \cdot b}{|a||b|}=cos^{-1}\dfrac{-5}{\sqrt {5}\sqrt {10}}$ $=arccos \frac{-5}{ \sqrt {50}}$ $=arccos \frac{-1}{\sqrt 2}$ $= arccos \frac{-\sqrt 2}{2}$ $=\frac{3 \pi}{4}$ $=135 ^ \circ$ Subtract from $180^ \circ$ to get acute angle. $180^ \circ-135 ^ \circ=45 ^ \circ$