Question

Using matrix method solve the following simultaneous equations

3x - 1y = 7

2x + 3y = 12

Answer #1

Augmented matrix for given system of equations

solution using Gauss-Jordan elimination

Your matrix

X1 | X2 | b | |
---|---|---|---|

1 | 3 | -1 | 7 |

2 | 2 | 3 | 12 |

Make the pivot in the 1st column by dividing the 1st row by 3

X1 | X2 | b | |
---|---|---|---|

1 | 1 | -1/3 | 7/3 |

2 | 2 | 3 | 12 |

Eliminate the 1st column

X1 | X2 | b | |
---|---|---|---|

1 | 1 | -1/3 | 7/3 |

2 | 0 | 11/3 | 22/3 |

Make the pivot in the 2nd column by dividing the 2nd row by 11/3

X1 | X2 | b | |
---|---|---|---|

1 | 1 | -1/3 | 7/3 |

2 | 0 | 1 | 2 |

Eliminate the 2nd column

X1 | X2 | b | |
---|---|---|---|

1 | 1 | 0 | 3 |

2 | 0 | 1 | 2 |

Solution set:

x1 = 3

x2 = 2

solve the following pairs of simultaneous equations
a) x=7y+3
y=3x-7
b) 2x+5y =23
5x-2y=14

Section B.3 - Algebra - Simultaneous and Quadratic Equations
Solve problems 1 and 2 using the comparison, elimination, or
substitution method.
1) x +y =2 2x -3y =5
2 ) 3x - 5y=5 7x + y = 75

Solve by matrix method
x-y+2z=7
3x+4y-5z=-5
2x-y+3z=12

Solve the following system of equations. 2x-3y+z=2 13x-7z=-5
3x+y=2

Solve the following system of equations by using the inverse of
the coefficient matrix.
7x?y+4z=?3
?3y+8z=?20
-2x+4y+5z=-42

4. Solve the system of linear equations by using the
Gauss-Jordan (Matrix) Elimination Method. No credit in use any
other method. Use exactly the notation we used in class and in the
text. Indicate whether the system has a unique solution, no
solution, or infinitely many solutions. In the latter case, present
the solutions in parametric form.
3x + 6y + 3z = -6
-2x -3y -z = 1
x +2y + z = -2

Solve the following system of equations using Matrix Algebra
with Excel
7X + 4Y - 8Z
= 50
5X
- 3Y + 5Z = 45
3X
+ 2Y + 2Z = 40

Solve this system of equations
−2x−3y=−17
−3x+2y=−6
One solution:
No solution
Infinite number of solutions

Solve the linear programming problem by the method of
corners.
Maximize
P = 2x + 3y
subject to
x
+
y
≤
10
3x
+
y
≥
12
−2x
+
3y
≥
11
x ≥ 0, y ≥ 0

Solve the following system of equations using Matrix
Algebra.
7X + 4Y - 8Z = 50
5X - 3Y + 5Z = 45
3X + 2Y + 2Z = 40
PLEASE USE EXCEL***

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