SOLUTION: I need help with this problem. I am supposed to solve this system using determinants and I am getting reallly confused!! 7x+3y=1 3x + 4y= 5 help :)

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Question 1084469: I need help with this problem. I am supposed to solve this system using determinants and I am getting reallly confused!!
7x+3y=1
3x + 4y= 5
help :)
Found 2 solutions by Boreal, MathLover1:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
det a====b
===c====d
Here, the determinant is a--b
-------------------------c--d, where a is the 7 in 7x and b the 3 in 3y, c is 3 in 3x and d is 4 in 4y.
The determinant is found by multiplying ad and subtracting cd, and that will be the denominator.
det of 7==3
=====3==4
is 28-9=19
To solve for x,
now put the 1 and 5 into the first column, and make a new determinant:
1====3
5====4
That product is 4-15=-11
so x=-11/19.
To get y, put the 1 and 5 into second column
7====1
3====5
so y=32/19
check -77/19+96/19=19/19=1
-33/19+128/19=95/19=5

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
7x%2B3y=1
3x+%2B+4y=+5

matrix%282%2C3%2C7%2C3%2C1%2C3%2C4%2C5%29

first find a "coefficient matrix"
matrix%282%2C2%2Ca%2Cb%2Cc%2Cd%29

determinant is defined to be D=ad+-+bc
in your case a=7,b=3,c=3, and d=4
D=7%2A4+-+3%2A3=28-9=19
now,delete the column for the x coefficients and use constants to find determinant D%5Bx%5D
matrix%282%2C2%2C1%2C5%2C3%2C4%29
D%5Bx%5D=4-+15=-11
do same for the y coefficients and use constants to find determinant D%5By%5D
matrix%282%2C2%2C5%2C3%2C1%2C7%29-> D%5By%5D=35-3=32
now find x and y:
x=D%5Bx%5D%2FD=-11%2F19
y=D%5By%5D%2FD=+32%2F19+