Unit Vector Notation: Solve a1, a2 for Vector Equation

[saber1357]

Homework Statement

Vector a1 + vector a2 = 5*vector a3
Vector a1 - vector a2 = 3*vector a3
Vector a3 = 2i + 2j (i and j are the vector components)
Express 1) vector a1 and 2) vector a2 in unit vector notation

Homework Equations

Vector R = Ax + Yx

The Attempt at a Solution

I took the first equation and replaces the a3 with 2i+2j, so vector a1 + vector a2 = 5(2i + 2j)
a1 + a2 = 10i + 10j
I solved for R and found direction, but I do'nt believe that helps at all. (R = sqr root of 200 and direction was 45 degrees).
From the first equation with addition, I could conclude that vector a1 could equal = 10i +0j and vector a2 could equal 0i + 10j. However, these values don't work for the second equation with the subtraction. Is there some sort of secret to this problem?

 

[learningphysics]

Don't worry about magnitudes and angles for this problem. This one is straight algebra. substitute a3 into the second equation also. That'll give you another equation with a1 and a2.

You have two equations with two unknowns (a1 and a2)... solve those, get a1 and a2.