Finding the value of x in vector equations

I have a basic trig background and am struggling with this particular equation:

(x+2)i+(2y-1)j=yi+3xj

The objective of the equation is find the value of x. How do I go about that?

[Walter Roberson]

Are i and j both real-valued unknowns?

Are i and j both names for the same sqrt(-1) ?

Is i sqrt(-1) and j is sqrt(-1) "in a different direction" ?

Is i a unit vector on the y axis and j is a unit vector on the z axis?

Is i a unit vector on the x axis and j is a unit vector on the y axis?

[Katherine Fanning]

i is a unit vector on the x axis, j is a unit vector on the y axis.

Answer 1

[Walter Roberson]

     (-8*x-4)*i + (y+9)j = 9*y*i -7*x*j
     
     i and j are independent so you can separate the variables
     
     (-8*x-4)*i = 9*y*i
     (y+9)*j = -7*x*j
     
     Remove the units
     
     -8*x-4 = 9*y
     y+9 = -7*x
     
     isolate y. Second equation is easier
     
     y+9 = -7*x -> y = -7*x - 9
     
     Substitute into the other equation
     
     -8*x - 4 = 9*(-7*x - 9)
     
     Expand
     
     -8*x - 4 = -63*x - 81
     
     isolate x
     
     -8*x + 63*x = -81 + 4
     55 * x = -77
     x = -77/55