Answer
$$\langle2,-3\rangle$$
Work Step by Step
To scale a vector in component form, multiply each component by the scale factor.
$$2\vec{u}=2\langle -5,3\rangle=\langle 2\times (-5),2\times 3\rangle=\langle-10,6\rangle.$$
$$3\vec{v}=3\langle 4,-3\rangle=\langle 3\times 4,3\times (-3)\rangle=\langle12,-9\rangle$$
To add vectors in component form, add x and y components separately.
$$2\vec{u}+3\vec{v}=\langle -10,6\rangle+\langle 12,-9\rangle=\langle -10+12,6-9\rangle=\langle2,-3\rangle$$
