Find an equation of the plane that passes through the points $(0-2,5)$ and $(-1,3,1)$ and is perpendicular to the plane $2z = 5x + 4y$.
Here's what I have so far:
The plane through $(0,-2,5)$ is $ax + b(y+z) + c(z-5) = 0$. And the plane also passes through $(-1,3,1)$ so I get: $-a + 5b - 4c = 0 \tag{1}.$
When I looked at the explanation it says:
Now we know that the plane is perpendicular to $5x + 4y - 2z = 0$ and then it replaces $(x,y,z)$ with $(a,b,c)$ to get $5a + 4b - 2c = 0. \tag{2}$
It continues from there saying to solve the two equations to get $\frac{a}{6} = \frac{b}{-22} = \frac{c}{-29}$.
I know how to solve it once it gets to this but I have absolutely no idea how they got to this step.