SOLUTION: Using matrices to solve systems of equations I have the problem 4x+3y=7, -2x+4y=24. While I think the answer is (-2, 5), I can't figure out what to do next after finding the det

Algebra ->  Matrices-and-determiminant -> SOLUTION: Using matrices to solve systems of equations I have the problem 4x+3y=7, -2x+4y=24. While I think the answer is (-2, 5), I can't figure out what to do next after finding the det      Log On


   

Question 1115457: Using matrices to solve systems of equations
I have the problem 4x+3y=7, -2x+4y=24. While I think the answer is (-2, 5), I can't figure out what to do next after finding the determinant ( - 1/5 ). Thanks!
Answer by ikleyn(52829) About Me  (Show Source):
You can put this solution on YOUR website!
.
det   = det %28matrix%282%2C2%2C+4%2C3%2C+-2%2C4%29%29 = 4*4 - (-2)*3 = 16+6 = 22.


det_X = det %28matrix%282%2C2%2C+7%2C3%2C++24%2C4%29%29 = 7*4 - 3*24 = -44;   x = det_X%2Fdet = %28-44%29%2F22 = -2.


det_Y = det %28matrix%282%2C2%2C+4%2C7%2C++-2%2C24%29%29 = 4*24 - (-2)*7 = 110;   y = det_Y%2Fdet = 110%2F22 = 5.


Answer.  x= -2;  y= 5.

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On solving 2x2-linear systems using determinants 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.