Intersection of planes/3x+4y+5z is 2 and 2x-y+3z is -1/Line equation/Exercise

Consider in ${}\mathbb {R} ^{3}$ the two planes

$E={\left\{(x,y,z)\in \mathbb {R} ^{3}\mid 3x+4y+5z=2\right\}}{\text{ and }}F={\left\{(x,y,z)\in \mathbb {R} ^{3}\mid 2x-y+3z=-1\right\}}.$

Determine the intersecting line ${}E\cap F$.

Create a solution