<prompt> Ke mekhoa efe e tloaelehileng ea ho rarolla tsamaiso ea li-equation tsa linear?nan  <response>: Instruction in English: What are the common techniques for solving a system of linear equations? . Response in English: There are several common techniques for solving systems of linear equations, including the following:1. Graphing: One way to solve a system of linear equations is to graph the equations on the same set of axes and see where they intersect. The x- and y-coordinates of the intersection point are the solutions to the system.2. Substitution: This method involves solving for one variable in one equation, then substituting that solution into the other equation to solve for the remaining variable. After finding the value of one variable, you can substitute it back into one of the equations to obtain the value of the other variable.3. Elimination: This method involves adding or subtracting the equations to eliminate one of the variables. Once one variable is eliminated, you can solve for the remaining variable. After finding the value of one variable, you can substitute it back into one of the equations to obtain the value of the other variable.4. Gaussian elimination: This method involves using row operations to transform the augmented matrix of the system into an equivalent matrix in echelon form. Then, back substitution is used to solve for the variables.5. Matrix methods: Systems of linear equations can also be solved using matrix methods such as the inverse matrix method or Cramers rule. These methods involve using matrix algebra to represent and solve the system of equations.Regardless of the method used, the underlying goal is to find the values of the variables that make all the equations in the system true simultaneously. . Response in Sesotho: Ho na le mekhoa e maloa e tloaelehileng ea ho rarolla litsamaiso tsa li-equation tsa mela, ho kenyeletsoa tse latelang: 1. Kerafo: Tsela e ngoe ea ho rarolla mokhoa oa li-equation tsa mela ke ho etsa kerafo ea li-equation sete e tšoanang ea lilepe le ho bona moo li kopanang teng. Likhokahanyo tsa x- le y tsa ntlha ea mateano ke tharollo ea sistimi. 2. Phapanyetsano: Mokhoa ona o kenyelletsa ho rarolla phapang e le ngoe ho equation e le ngoe, ebe o kenya tharollo ho equation e ngoe ho rarolla phapang e setseng. Kamora ho fumana boleng ba mofuta o le mong, o ka o khutlisetsa ho e ngoe ea li-equations ho fumana boleng ba mofuta o mong. 3. Pheliso: Mokhoa ona o kenyelletsa ho eketsa kapa ho fokotsa lipalo ho felisa e ngoe ea mefuta e fapaneng. Hang ha phapang e le ngoe e felisitsoe, u ka khona ho rarolla phapang e setseng. Kamora ho fumana boleng ba mofuta o le mong, o ka o khutlisetsa ho e ngoe ea li-equations ho fumana boleng ba mofuta o mong. 4. Ho felisoa ha Gaussian: Mokhoa ona o kenyelletsa ho sebelisa tsebetso ea mela ho fetola matrix a eketsehileng a tsamaiso hore e be matrix a lekanang ka mokhoa oa echelon. Ka mora moo, sebaka sa morao se sebelisetsoa ho rarolla mefuta-futa. 5. Mekhoa ea matrix: Mekhoa ea li-linear equations e ka boela ea rarolloa ho sebelisoa mekhoa ea matrix e kang mokhoa o fapaneng oa matrix kapa molao oa Cramer. Mekhoa ena e kenyelletsa ho sebelisa matrix algebra ho emela le ho rarolla tsamaiso ea lipalo. Ho sa tsotellehe mokhoa o sebelisoang, sepheo sa motheo ke ho fumana litekanyetso tsa mefuta-futa e etsang hore lipalo tsohle tsa tsamaiso li be nete ka nako e le ngoe. 