Introduced 81104

The * (asterisk) operation assigning one number to two pairs of numbers is introduced as follows:

(a, b)*(c, d) = ac+bd

We know that:
(x,2)*(-1, v) = -1 and (2,-1)*(u, v)=5 and (u, v)*(1,1)=-2

What is (1,2)*(x, y) equal to if y=3?

Correct answer:

w =  1

Step-by-step explanation:

y=3 (1,2) (x, y) = 1 x+2 y = x+6  (a, b) (c, d) = ac+bd = (c, d) (a,b)  x+2v=1 2uv=5 u+v=2  x+2 v=1 2 uv=5 u+v=2  2vx=1 2uv=5 u+v=2  Pivot:Row1Row2 2uv=5 2vx=1 u+v=2  Row321 Row1Row3 2uv=5 2vx=1 1.5v=4.5  Row321.5 Row2Row3 2uv=5 2vx=1 0.75x=3.75  x=0.753.75=5 v=21+x=215=3 u=25+v=253=1  u=1 v=3 x=5  w=x+2 y=(5)+2 3=1



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