SOLUTION: 1. Solve the given system by Cramer’s Rule : 5x1+ 4x2 = -14 3x1+ 6x2 = 6

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Question 1156102: 1. Solve the given system by Cramer’s Rule :
5x1+ 4x2 = -14
3x1+ 6x2 = 6
Answer by ikleyn(52933) About Me  (Show Source):
You can put this solution on YOUR website!
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First, calculate the determinant of the coefficient matrix

    D = det %28matrix%282%2C2%2C+5%2C4%2C+3%2C6%29%29 = 5*6 - 3*4 = 30 - 12 = 18.



Next, calculate the determinant Dx, replacing first column in the coefficient matrix by the right side vector

    Dx = det %28matrix%282%2C2%2C+-14%2C4%2C++6%2C6%29%29 = -14*6 - 4*6 = -84 - 24 = -108.



Next, calculate the determinant Dy, replacing second column in the coefficient matrix by the right side vector

    Dy = det %28matrix%282%2C2%2C+5%2C-14%2C++3%2C6%29%29 = 5*6 - (-14)*3 = 30 - (-42) = 72.



Now the solution is  x = Dx%2FD = -108%2F18 = -6;  y = Dy%2FD = 72%2F18 = 4.



ANSWER.  x = -6,  y = 4.

Solved.

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On Cramer's rule for solving 2x2-system of equations, see the lesson

    - Solution of the linear system of two equations in two unknowns using determinant

and 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.