Solve x y=42x-5y=15 - ScanMath

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Question

Solve the system of equations

(x_{1}, y_{1}) = (\frac{5 + 5 57}{28}, \frac{- 3 + 3 57}{2}) (x_{2}, y_{2}) = (\frac{5 - 5 57}{28}, - \frac{3 + 3 57}{2})

Evaluate

{x y = 42 x - 5 y 42 x - 5 y = 15

Solve the equation for x

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{x y = 42 x - 5 y x = \frac{15 + 5 y}{42}

Substitute the given value of x into the equation x y = 42 x - 5 y

\frac{15 + 5 y}{42} \times y = 42 \times \frac{15 + 5 y}{42} - 5 y

Simplify

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\frac{y ( 15 + 5 y )}{42} = 42 \times \frac{15 + 5 y}{42} - 5 y

Simplify

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\frac{y ( 15 + 5 y )}{42} = 15

Cross multiply

y (15 + 5 y) = 42 \times 15

Simplify the equation

y (15 + 5 y) = 630

Expand the expression

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15 y + 5 y^{2} = 630

Move the expression to the left side

15 y + 5 y^{2} - 630 = 0

Rewrite in standard form

5 y^{2} + 15 y - 630 = 0

Substitute a= 5,b= 15 and c= - 630 into the quadratic formula y = \frac{- b \pm b ^{2} - 4 a c}{2 a}

y = \frac{- 15 \pm 1 5 ^{2} - 4 \times 5 ( - 630 )}{2 \times 5}

Simplify the expression

y = \frac{- 15 \pm 1 5 ^{2} - 4 \times 5 ( - 630 )}{10}

Simplify the expression

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y = \frac{- 15 \pm 12825}{10}

Simplify the radical expression

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y = \frac{- 15 \pm 15 57}{10}

Separate the equation into 2 possible cases

y = \frac{- 15 + 15 57}{10} y = \frac{- 15 - 15 57}{10}

Simplify the expression

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y = \frac{- 3 + 3 57}{2} y = \frac{- 15 - 15 57}{10}

Simplify the expression

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y = \frac{- 3 + 3 57}{2} y = - \frac{3 + 3 57}{2}

Evaluate the logic

y = \frac{- 3 + 3 57}{2} \cup y = - \frac{3 + 3 57}{2}

Rearrange the terms

{x = \frac{15 + 5 y}{42} y = \frac{- 3 + 3 57}{2} \cup {x = \frac{15 + 5 y}{42} y = - \frac{3 + 3 57}{2}

Calculate

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{x = \frac{5 + 5 57}{28} y = \frac{- 3 + 3 57}{2} \cup {x = \frac{15 + 5 y}{42} y = - \frac{3 + 3 57}{2}

Calculate

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{x = \frac{5 + 5 57}{28} y = \frac{- 3 + 3 57}{2} \cup {x = \frac{5 - 5 57}{28} y = - \frac{3 + 3 57}{2}

Check the solution

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{x = \frac{5 + 5 57}{28} y = \frac{- 3 + 3 57}{2} \cup {x = \frac{5 - 5 57}{28} y = - \frac{3 + 3 57}{2}

Check the solution

More Steps

{x = \frac{5 + 5 57}{28} y = \frac{- 3 + 3 57}{2} \cup {x = \frac{5 - 5 57}{28} y = - \frac{3 + 3 57}{2}

Solution

(x_{1}, y_{1}) = (\frac{5 + 5 57}{28}, \frac{- 3 + 3 57}{2}) (x_{2}, y_{2}) = (\frac{5 - 5 57}{28}, - \frac{3 + 3 57}{2})

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