Linear Equations

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Can you please help solve this equation using the substitution method? I have tried and keep getting that X and Y = 7/2, but the answer in the book states no solution, inconsistent system. What am I doing wrong? Please help! Solve the systems of equations by the substitution method.
y-x=4
x-y=3
Thank you!

  • Linear Equations -

    Here is why there is no solution ...

    multiply the first equation by -1
    x - y = -4
    subtract the second equation ...
    0 = -7 >>>> CONTRADICTION! So, no solution.

    OR
    by substitution,
    first equation: y = x+4
    sub into second
    x-y = 3
    x - (x+4) = 3
    x-x-4=3
    0 = 7, same result.

    Your answer of x = y = 7/2 does not work in either equation.

  • Linear Equations -

    Solve the following system of equations by the substitution method.

    8x = 2y + 5
    3x = y + 7

  • Linear Equations -

    Y-X=4...(EQN 1)
    X-Y=3...(EQN 2)
    MAKING X THE SUBJECT IN EQN 2
    X=3+Y
    SUBSTITUTING IN EQN 1
    Y-(3+Y)=4
    Y-3-Y=4
    THE Y GETS ELIMINATED,HENCE THERE IS NO SOLUTION

  • Linear Equations -

    x=4,y=0

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