SOLUTION: Determine the x-coordinate of the solution to the system of equations: x + 8y = - 29 - 7x + 7y = - 37

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Question 1121799: Determine the x-coordinate of the solution to the system of equations:
x + 8y = - 29
- 7x + 7y = - 37
Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
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Use the Cramer's rule:


x = det_x%2Fdet,


where det = determinant of the coefficient matrix  det %28matrix%282%2C2%2C+1%2C8%2C+-7%2C7%29%29 = 1*7 - 8*(-7) = 7 + 56 = 63,


det_x = determinant of the matrix obtained by replacing the first column of the coefficient matrix by the right side vector =


      = det %28matrix%282%2C2%2C+-29%2C8%2C++-37%2C7%29%29 = -29*7 - 8*(-37) = 93.


So,  x = 93%2F63 = 31%2F21.


Answer.  31%2F21.

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On Cramer's rule for solving systems of 2 equations in 2 unknowns 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.

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

The referred lessons are the part of this online textbook under the topic
     "2x2-Matrices, determinants, Cramer's rule for systems in two unknowns"


Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.