What is the Simplified Form of Cramer's Rule for Solving for y?

In summary, Use Cramer's rule to solve for y in a system of linear equations. The formula for Cramer's rule is y = det[coefficients of x and y]/det[coefficients of x and y]. For part (a), the solution is y = -c/(ad-bc). For part (b), the solution is y = (fg-di)/(aei+bfg+cdh-ceg-afh-ibd).
  • #1
tatianaiistb
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Homework Statement



Use Cramer's rule to solve for y (only). Call the 3x3 determinant D:

(a) ax+by = 1
cx+dy=0

(b) ax+by+cz=1
dx+ey+fz=0
gx+hy+iz=0

Homework Equations



Cramer's Rule: x=A-1*b



The Attempt at a Solution



(a) So far I have,

y= [det [a 1; c 0] / det [a b; c d]} = (0-c)/(ad-bc)=-c/(ad-bc)

I don't know how to proceed...

Same with part (b),

y= [det[a 1 c; d 0 f; g o i]/det[a b c; d e f; g h i]] = (fg-di)/(aei+bfg+cdh-ceg-afh-ibd)

Is there a way to simplify this?
 
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  • #2
You're done.
 

FAQ: What is the Simplified Form of Cramer's Rule for Solving for y?

1. What is Cramer's Rule?

Cramer's Rule is a method used to solve systems of linear equations. It involves using determinants to find the unique solution for a variable in the system.

2. How is Cramer's Rule used to solve for y?

Cramer's Rule involves setting up a matrix with the coefficients of the equations and a column matrix with the constants. Then, the determinant of the coefficient matrix is divided by the determinant of the entire system to find the value of y.

3. When is Cramer's Rule most useful?

Cramer's Rule is most useful when there are only two variables in the system of equations. It can also be useful when the equations are not too complex and the determinants can be easily calculated.

4. What are the limitations of Cramer's Rule?

Cramer's Rule can be time-consuming and tedious to use for systems with more than two variables. It is also limited by the need for non-zero determinants in order for the rule to work.

5. Are there any alternative methods to using Cramer's Rule?

Yes, there are other methods such as substitution, elimination, and Gaussian elimination that can also be used to solve systems of linear equations. These methods may be more efficient and practical for more complex systems.

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