Question 251325
How do you solve a substitution problem using matrices?
ex....         5x+2y=-8 and 4x+3y+2
5x+2y=-8
4x+3y=-2
Soln:
I am new to this group, so i will not be able to write matrices like (). will try to explain:
Here you will use cramer's Rule like this:
You will create three matrices. One with the elements (row wise)
1st row: 5  2
2nd row: 4  3
you will calculate the value of determinant(D) as (5*3 minus 4*2)=7
then we will replace first column i.e. 5 and 4 with -8 and 2
so it will be like
1st row: -8  2
2nd row: -2  3
again we will calucate the value and call it as D1: -8*3 minus -2*2
so D1=-20
now we will calculate D2 by replacing 2nd column with -8 and 2
so matrix will be like
1st row: 5  -8
2nd row: 4  -2
so D2=5*(-2) minus 4*(-8)=22

now we have D=7,D1=-20,D2=22
and x=D1/D and y=D2/D.

so x=-20/7 and y=22/7

Hope it will be clear