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Find the equation: a) (2x-3y+4)/4 = 0 b) -(x+2y)/5x = 1 c) (2x-3y+4)/4 = 4

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3 parts
a

2x - 3y + 4 = 0\textbf{2x - 3y + 4 = 0}

b

3x + y = 0\textbf{3x + y = 0}

c

2x - 3y - 12 = 0\textbf{2x - 3y - 12 = 0}

Step-by-step solution

9 steps

here are the solutions for finding the equations.

Part a· 2 steps

2x−3y+44=0\frac{2x - 3y + 4}{4} = 0

  1. Multiply both sides of the equation by 4 to eliminate the denominator.

    4×(2x−3y+44)=0×44 \times \left(\frac{2x - 3y + 4}{4}\right) = 0 \times 4 2x−3y+4=02x - 3y + 4 = 0

  2. The equation is already in the standard form Ax+By+C=0Ax + By + C = 0.

    The equation is 2x - 3y + 4 = 0\boxed{\textbf{2x - 3y + 4 = 0}}.

Part b

3x + y = 0\textbf{3x + y = 0}

−(x+2y)5x=1\frac{-(x + 2y)}{5x} = 1

  1. Multiply both sides of the equation by $5x$ to eliminate the denominator.

    5x×(−(x+2y)5x)=1×5x5x \times \left(\frac{-(x + 2y)}{5x}\right) = 1 \times 5x −(x+2y)=5x-(x + 2y) = 5x

  2. Distribute the negative sign on the left side.

    −x−2y=5x-x - 2y = 5x

  3. Move all terms involving xx and yy to one side of the equation.

    Add xx to both sides.

    −2y=5x+x-2y = 5x + x −2y=6x-2y = 6x

  4. Rearrange to a standard form, for example, Ax+By=0Ax + By = 0.

    6x+2y=06x + 2y = 0

  5. Divide by the common factor of 2 to simplify.

    3x+y=03x + y = 0

    The equation is 3x + y = 0\boxed{\textbf{3x + y = 0}}.

Part c

2x - 3y - 12 = 0\textbf{2x - 3y - 12 = 0}

2x−3y+44=4\frac{2x - 3y + 4}{4} = 4

  1. Multiply both sides of the equation by 4 to eliminate the denominator.

    4×(2x−3y+44)=4×44 \times \left(\frac{2x - 3y + 4}{4}\right) = 4 \times 4 2x−3y+4=162x - 3y + 4 = 16

  2. Subtract 16 from both sides to set the equation to Ax+By+C=0Ax + By + C = 0 form.

    2x−3y+4−16=02x - 3y + 4 - 16 = 0 2x−3y−12=02x - 3y - 12 = 0

    The equation is 2x - 3y - 12 = 0\boxed{\textbf{2x - 3y - 12 = 0}}.

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