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solvefor y,m=(y^2-y^1)/(x^2-x^1)

Solution

solve for

y, m = \frac{y ^{2} - y ^{1}}{x ^{2} - x ^{1}}

Solution

y = \frac{1 + 1 - 4 ( m x - m x ^{2} )}{2}, y = \frac{1 - 1 - 4 ( m x - m x ^{2} )}{2}

Solution steps

m = \frac{y ^{2} - y ^{1}}{x ^{2} - x ^{1}}

Simplify

x^{2} - x^{1} : x^{2} - x

m = \frac{y ^{2} - y ^{1}}{x ^{2} - x}

Multiply both sides by

x^{2} - x

m (x^{2} - x) = y^{2} - y; x \neq = 1, x \neq = 0

Expand

m (x^{2} - x) : m x^{2} - m x

m x^{2} - m x = y^{2} - y; x \neq = 1, x \neq = 0

Switch sides

y^{2} - y = m x^{2} - m x; x \neq = 1, x \neq = 0

Move

m x

to the left side

y^{2} - y + m x = m x^{2}; x \neq = 1, x \neq = 0

Move

m x^{2}

to the left side

y^{2} - y + m x - m x^{2} = 0; x \neq = 1, x \neq = 0

Solve with the quadratic formula

y_{1, 2} = \frac{- ( - 1 ) \pm ( - 1 ) ^{2} - 4 \cdot 1 \cdot ( m x - m x ^{2} )}{2 \cdot 1}

Simplify

(- 1)^{2} - 4 \cdot 1 \cdot (m x - m x^{2}) : 1 - 4 (m x - m x^{2})

y_{1, 2} = \frac{- ( - 1 ) \pm 1 - 4 ( m x - m x ^{2} )}{2 \cdot 1}

Separate the solutions

y_{1} = \frac{- ( - 1 ) + 1 - 4 ( m x - m x ^{2} )}{2 \cdot 1}, y_{2} = \frac{- ( - 1 ) - 1 - 4 ( m x - m x ^{2} )}{2 \cdot 1}

y = \frac{- ( - 1 ) + 1 - 4 ( m x - m x ^{2} )}{2 \cdot 1} : \frac{1 + 1 - 4 ( m x - m x ^{2} )}{2}

y = \frac{- ( - 1 ) - 1 - 4 ( m x - m x ^{2} )}{2 \cdot 1} : \frac{1 - 1 - 4 ( m x - m x ^{2} )}{2}

The solutions to the quadratic equation are:

y = \frac{1 + 1 - 4 ( m x - m x ^{2} )}{2}, y = \frac{1 - 1 - 4 ( m x - m x ^{2} )}{2}

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