\left.\begin{array}{l}{[\text { Coordinate Method in Space }]} \\ {[\text { Parametric Equations of a Line }]\end{array}\right]

Derive the parametric equations of the line of intersection of the planes $2 x-y-3 z+5=0$ and $x+y-2=0$.
Let $x=t$ and solve for $y$ and $z$ the system of equations

$$
\left\{\begin{array}{l}
y+3 z=2 t+5 \\
y=-t+2
\end{array}\right.
$$

We get:

$$
\left\{\begin{array}{l}
x=t \\
y=2-t \\
z=1+t
\end{array}\right.
$$

## Answer

$x=t, y=2-t, z=1+t$