SOLUTION: Please help me here. Ax+By=C Dx+Ey=F Solve the system for x and y I got x=C-By/A y= (AF-CD)/(AE-BD) Not sure if I am right. Thank you.

Question 1090975: Please help me here.
Ax+By=C
Dx+Ey=F
Solve the system for x and y
I got x=C-By/A
y= (AF-CD)/(AE-BD)
Not sure if I am right.
Thank you.
Found 2 solutions by jim_thompson5910, ikleyn:
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!

You can use Cramer's Rule to solve this. Let's define the following

P = the matrix (notice it's the left hand side coefficients)

Px = the matrix . I started with matrix P and I've replaced the first column with C and F, both of which are the right hand side values

Py = the matrix . I started with matrix P ann replaced the second column with C and F, both of which are the right hand side values

The notation det(P) is the determinant of matrix P. Using the two-by-two matrix determinant rule we can say

Then you divide the determinants to get x and y

If we knew the values of A,B,C,D,E, and F, then we could compute the actual numeric values of x and y. However, since we don't know those six variables, we just leave it as shown above.

So the final answers are

Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
.
On the Cramer's rule on solving systems of 2 linear equations in 2 unknowns see the lesson
    - Solution of the linear system of two equations in two unknowns using determinant
in this site.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this online textbook under the topic "Systems of two linear equations in two unknowns".

Also, see the lessons
    - What is a matrix?,
    - Determinant of a 2x2-matrix,
    - HOW TO solve system of linear equations in two unknowns using determinant (Cramer's rule),
    - Solving systems of linear equations in two unknowns using the Cramer's rule,
in this site.

The referred lessons are the part of the other online textbook
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.
under the topic "2x2-Matrices, determinants, Cramer's rule for systems in two unknowns"

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