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Cramer's Rule - HELP! Please












































Use Cramer's rule to solve the system

x−6y=20
3x+2y=0

x=
y=

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Mar 26, 2011
Cramer's Rule – Solve for 2 Unknowns
by: Staff


The question:

Use Cramer's rule to solve the system

x−6y=20
3x+2y=0

x=
y=


The answer:

Cramer’s rule allows you to solve for either variable (x or y) separately, without solving the entire system of linear equations.


System of Equations

x−6y=20

3x+2y=0

We are not going to use an augmented matrix. Instead, I have listed two separate matrices.

Coefficient Matrix

1 -6
3 2

Constant Matrix

20
0

Step 1: Compute the determinant for the Coefficient Matrix


Sample 2 x 2 matrix

a b
c d

the Determinant of Sample Matrix

Det(Sample Matrix) = a*d - c*b

Coefficient Matrix

1 -6
3 2

Det(Coefficient Matrix) = 1*2 – 3*(-6)

Det(Coefficient Matrix) = 20




Step 2: To SOLVE for x, replace the first column in the coefficient matrix with the constant matrix, then compute the determinant of the new matrix

20 -6
0 2

Det(x Matrix) = 20*2 – 0*(-6)

Det(x Matrix) = 40

Cramer's Rule states:

x = Det(x Matrix) ÷ Det(Coefficient Matrix)

x = 40 ÷ 20

x = 2

Step 3: To SOLVE for y, replace the second column in the coefficient matrix with the constant matrix, then compute the determinant of the new matrix

1 20
3 0

Det(y Matrix) = 1*0 - 3*(20)

Det(y Matrix) = -60

Cramer's Rule states:

y = Det(y Matrix) ÷ Det(Coefficient Matrix)

y = -60 ÷ 20

y = -3

the final answer to your question is:

x = 2

y = -3


Check the answer by substituting the numerical values of x, and y into the original equations:

x - 6y = 20

2 - 6*(-3) = 20 , correct


3x + 2y = 0


3*2 + 2*(-3) = 0, correct


Since the numerical values of x, and y, work in both of the original equations, the solutions are correct.




Thanks for writing.


Staff
www.solving-math-problems.com


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