Mathematics for Engineering Science and Technology PDF

Mathematics for Engineering Science and Technology COURSE CODE: MATH 0 PROGRAM NAME: BACHELOR OF SCIENCE IN MECHANICAL ENGINEERING (BSME) CREDIT UNITS : 1 UNIT (LAB)  Topic 5 Systems of Linear Equations Concept of a Systems of Linear Equations...

Mathematics for Engineering Science and Technology COURSE CODE: MATH 0 PROGRAM NAME: BACHELOR OF SCIENCE IN MECHANICAL ENGINEERING (BSME) CREDIT UNITS : 1 UNIT (LAB)  Topic 5 Systems of Linear Equations Concept of a Systems of Linear Equations Frequently in problems dealing with two related quantities, it is difficult to represent the quantities in terms of only one unknown. However, if two unknowns are used, two equations containing the unknowns can be formulated and solved together. A pair of values must be found which satisfies both equations called simultaneous equations. The solution may be done algebraically and graphically.  System of Linear Equations Definition of Terms Linear Equations – first-degree equations with two unknowns. The graphs of these equations are straight lines. Inconsistent Equations – the graphs of two given equations are parallel lines. They do not have a common solution. Dependent Equations – the graphs of two given equations coincide or form the same line. They have many common solutions. Consistent – a system of equations. There is always a unique solution that is, the graph consists of intersecting lines. Solution of a System – in linear equation; is a pair of values of the unknowns or variables that will satisfy each of the equation in the system. Checking an Equation – means testing whether the pair of values will satisfy the equations, and to check, substitute the values of the variables in the given equation. If the resulting answers of the two members are the same, the pair of values is the root of the equation.  System of Linear Equations Solutions of Systems of Linear Equations Solution by Addition or Subtraction Procedure 1. Multiply one or both of the equations by a certain number that will give one of the unknowns the same coefficient in both equations. 2. If the coefficients have like signs, subtract one equation from the other, and if the coefficients have unlike signs, add the equations, thus eliminating one of the unknowns. 3. Solve the resulting equation for the remaining unknown. 4. Substitute the value obtained in (3) in any of the given equations containing the two unknowns to find the value of the other unknown. 5. Check the equations by substituting the values in the given equations.  System of Linear Equations Solutions of Systems of Linear Equations Solution by Addition or Subtraction  System of Linear Equations Solutions of Systems of Linear Equations Solution by Substitution Procedure 1. Select the easier equation and express one of the unknowns in terms of the second unknown. 2. Substitute the expression obtained in (1) in the other equation. 3. Solve the resulting equation to find the value of the second unknown. 4. Substitute the value of the second unknown in (1) to find the value of the first unknown. 5. Check the equation by substituting both values in the given equations.  System of Linear Equations Solutions of Systems of Linear Equations Solution by Substitution  System of Linear Equations Solutions of Systems of Linear Equations Solution by Comparison Procedure 1. From each equation find the value of one of the unknowns in terms of the other. 2. Form a new equation from these equal values. 3. Solve the resulting equation to find the value of the first unknown. 4. Substitute the value obtained in step 3 in one of the given equations to find the value of the second unknown. 5. Check the equation by substituting the values obtained in the two given equations.  System of Linear Equations Solutions of Systems of Linear Equations Solution by Comparison End of Topic 05