30.03.2023 - 13:25

How to solve a system of equations algebraically.

How to solve a system of equations algebraically.

Answers (1)
  • dzhaak
    April 3, 2023 в 20:12

    To solve a system of equations algebraically, you need to use a combination of techniques such as substitution, elimination, or matrix operations, depending on the type of system and the number of variables involved. The basic idea is to manipulate the equations so that you can isolate one variable in terms of the others and then substitute that expression into the other equations until you have a single equation with only one variable.

    For example, consider the system of equations:

    2x + 3y = 7 x - y = 1

    One way to solve this system is to use the substitution method. Solve one of the equations for one variable and substitute that expression into the other equation. For instance, you can solve the second equation for x:

    x = y + 1

    Then substitute that expression into the first equation, replacing x:

    2(y + 1) + 3y = 7

    Simplify and solve for y:

    2y + 2 + 3y = 7 5y + 2 = 7 5y = 5 y = 1

    Now, substitute this value of y back into either equation to find x:

    x - 1 = 1 x = 2

    Therefore, the solution to the system of equations is x = 2 and y = 1.

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