SOLUTION: Find the value of x+y in the following [3x-2] [x y] = [42 4] ..........[3 4] *I added the dots so the 3 and 4 could go under the x and y as one matrix

Algebra ->  Matrices-and-determiminant -> SOLUTION: Find the value of x+y in the following [3x-2] [x y] = [42 4] ..........[3 4] *I added the dots so the 3 and 4 could go under the x and y as one matrix      Log On


   

Question 190068: Find the value of x+y in the following
[3x-2] [x y] = [42 4]
..........[3 4]


*I added the dots so the 3 and 4 could go under the x and y as one matrix
Answer by cutepiscean5(19) About Me  (Show Source):
You can put this solution on YOUR website!
Find the value of x+y in the following
[3x-2] [x y] = [42 4]
..........[3 4]
Solution:
_________
we have a 1x2 matrix multiplied with a 2x2 matrix, which results in a 1x2 matrix again.
So, we first take the Left and side of this equation and multiply both the matrices and get the answers in terms of x and y.
we have:
[3x -2] [x y]
...............[3 4]
=>
we have got two terms which have been determined by multiplication, we now simplify them...
first element of the row is +%28+3x%5E2+-+6+%29+
and, second element of the row is +%28+3xy+-+8+%29+
now we compare both sides of the original equation and we get:
+3x%5E2+-+6+=+42+ ..........(1)
and
+3xy+-+8+=+4+ ............(2)
we have two equations and two variables x & y, we solve for them.
from equation (1) we have:
+3x%5E2+-+6+=+42+
=> +3x%5E2+=+42+%2B+6+
=> +3x%5E2+=+48+
=> +x%5E2+=+48%2F3+
=> +x%5E2+=+16+
=> +highlight%28x+=+4%29+ or +highlight%28x+=+-4%29+
From equation (2),
when we plug in x = 4 , we get:
+3xy+-+8+=+4+
=> +3%284%29y+-+8+=+4+
=> +12y++=+4+%2B+8+
=> +12y+=+12+
=> +y+=+12%2F12+
=> +highlight%28y=1%29+
when we plug in x = -4 , we get:
+3xy+-+8+=+4+
=> +3%28-4%29y+-+8+=+4+
=> +-12y++=+4+%2B+8+
=> +-12y+=+12+
=> +y+=+12%2F%28-12%29+
=> +highlight%28y=-1%29+
Thus x+y = 4+1 = +highlight%285%29+ or x+y = -4-1 = +highlight%28-5%29+
Hope this helps.