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Solve the system of equations: 2x − y = 6 and x − y = 1.

Mathematics

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Answer

x=5,y=4x=5, y=4

Step-by-step solution

5 steps

  1. Write down the given system of equations.

    Equation (1): 2x−y=62x - y = 6
    Equation (2): x−y=1x - y = 1

  2. Solve one of the equations for one variable in terms of the other.

    From Equation (2), it's easy to isolate xx:

    x=1+yx = 1 + y

  3. Substitute this expression into the other equation.

    Substitute x=1+yx = 1 + y into Equation (1):

    2(1+y)−y=62(1 + y) - y = 6

  4. Solve the resulting equation for yy.

    2+2y−y=62 + 2y - y = 6 2+y=62 + y = 6

    Subtract 2 from both sides:

    y=6−2y = 6 - 2 y=4y = 4

  5. Substitute the value of yy back into the expression for xx (from Step 2).

    x=1+yx = 1 + y x=1+4x = 1 + 4 x=5x = 5

    The solution to the system of equations is x=5x=5 and y=4y=4.

    The answer is x=5,y=4x=5, y=4.

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