simultaneous equations with three variables and three equations

simultaneous equations with three variables and three equations : is a system of three equations in the three variables x, y, z\,\! . A solution to a linear system is an assignment of numbers to the variables such that all .....   More from Wikipedia

  Homogeneous Linear Systems with Constant Coefficients: Solution via Matrix Eigenvalues (Real and Distinct Case). View the complete course: ocw.mit.edu License: Creative Commons BY-NC-SA More information at ocw.mit.edu More courses at ocw.mit.edu

Question : So I have to solve for x y and z given these three equations: 2x - y + z = 8 x + y - 2z = 5 x - y - z = -1 So I know your supposed to solve the equations for one variable or something but I'm not quite sure how to do this. If someone could show me steps in solving that would be great. Thank You

Answer : x + y - 2z = 5 x - y - z = -1 y cancels out leaving 2x -3z = 4 2x - y + z = 8 x + y - 2z = 5 y again cancels out leaving 3x -z = 13 2x -3z = 4 3x -z = 13 times the bottom by -3 leaving -9x + 3z = -39 2x -3z = 4 -9x + 3z = -39 z cancels and leaves -7x = -35 x=5 2x -3z = 4 3x -z = 13 plug x in to either equation 2(5) - 3z = 4 10 -3z = 4 3z = -6 z= -2 plug both z and x in to any equation 2x - y + z = 8 x + y - 2z = 5 x - y - z = -1 5 - y -(-2) = -1 5 - y +2 = -1 7 -y = -1 -y = -8 y= 8 plug all three into any equation to check your answers x - y - z = -1 5-8-(-2) = -1 -3 +2 = -1 -1 = -1 Answer: x= 5 y=8 z= -2..   More from Yahoo Answers

Question : Write a programme, using matrices, to solve simultaneous equations. You need only solve problems with two or three variables; For example: Two variables: 3x + 4y = 2, 7x - 3y = 5. Three variables: x - 2y + 3z = 6, 2x - y + z = 3, 3x + y - 2z = -1.The trick is to input the problem as a matrix problem, and then use the inverse of the matrix to solve it. In C programming language

Answer : #include #include using namespace std; #define rep(i, n) for((i) = 0; (i) < (n); (i)++) #define rep2(i, k, n) for((i) = k; (i) < (n); (i)++) void f21(); int n; double mat[100][100]; int main() { while(true) { cin >> n; if(!n) break; memset(mat, 0, sizeof(mat)); f21(); } return 0; } void f21() { cout << "****************************************" << endl; cout << "* INVERSE OF MATRIX *" << endl; cout << "****************************************" << endl; cout << "ORDER OF THE MATRIX: " << n << endl; cout << "ENTER ELEMENT ROW-WISE" << endl; int m = 2*n; int i, j, k; rep(i, n) { rep(j, n) { cin >> mat[i][j]; cout <<"\t"; printf("%5.3lf", mat[i][j]); } rep2(j, n, m) { if(i == (j-n)){ mat[i][j] = 1; continue; } mat[i][j] = 0; } cout << endl; } cout << endl << "INVERSE MATRIX: " << endl; double pivot, comm; rep(i, n) { pivot = mat[i][i]; if(mat[i][i] == 0){ cout << "DIVISION BY ZERO." <More from Yahoo Answers

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