For what values of t and s does the equality 2t 2 2s t 4s

For what values of t and s does the equality 2t + 2, 2s + t = 4s - 4t, - (2 + 5t) hold true? t = and s = At these values, the resulting vector is

Solution

(2t+2,2s+t)=(4s-4t, -(2+5t))

Two vectors are equal when their x components are equal to each other and y components are equal to each other

Therefore we get

2t+2=4s-4t and    2s+t=-(2+5t)

4s - 6t=2 and       2s +6t=-2

solving these two equations we get

s=0 and t=-1/3

And the resulting vector is (0,-1/3)