Solve 2x-y=10-x y=3

Question

Solve the system of equations

Solve using the substitution method

Solve using the elimination method

(x_{1}, y_{1}) = (\frac{17 + 65}{1 + 65}, \frac{- 3 + 65}{2}) (x_{2}, y_{2}) = (\frac{17 - 65}{1 - 65}, - \frac{3 + 65}{2})

Evaluate

{2 x - y = 10 - x y 10 - x y = 3

Solve the equation for x

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{x = \frac{10 + y}{2 + y} 10 - x y = 3

Substitute the given value of x into the equation 10 - x y = 3

10 - \frac{10 + y}{2 + y} \times y = 3

Multiply the terms

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10 - \frac{y ( 10 + y )}{2 + y} = 3

Move the constant to the right-hand side and change its sign

- \frac{y ( 10 + y )}{2 + y} = 3 - 10

Subtract the numbers

- \frac{y ( 10 + y )}{2 + y} = - 7

Rewrite the expression

\frac{- y ( 10 + y )}{2 + y} = - 7

Cross multiply

- y (10 + y) = (2 + y) (- 7)

Simplify the equation

- y (10 + y) = - 7 (2 + y)

Evaluate

y (10 + y) = 7 (2 + y)

Calculate

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10 y + y^{2} = 7 (2 + y)

Calculate

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10 y + y^{2} = 14 + 7 y

Move the expression to the left side

10 y + y^{2} - (14 + 7 y) = 0

Calculate the sum or difference

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3 y + y^{2} - 14 = 0

Rewrite in standard form

y^{2} + 3 y - 14 = 0

Substitute a= 1,b= 3 and c= - 14 into the quadratic formula y = \frac{- b \pm b ^{2} - 4 a c}{2 a}

y = \frac{- 3 \pm 3 ^{2} - 4 ( - 14 )}{2}

Simplify the expression

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y = \frac{- 3 \pm 65}{2}

Separate the equation into 2 possible cases

y = \frac{- 3 + 65}{2} y = \frac{- 3 - 65}{2}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

y = \frac{- 3 + 65}{2} y = - \frac{3 + 65}{2}

Evaluate the logic

y = \frac{- 3 + 65}{2} \cup y = - \frac{3 + 65}{2}

Rearrange the terms

{x = \frac{10 + y}{2 + y} y = \frac{- 3 + 65}{2} \cup {x = \frac{10 + y}{2 + y} y = - \frac{3 + 65}{2}

Calculate

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{x = \frac{17 + 65}{1 + 65} y = \frac{- 3 + 65}{2} \cup {x = \frac{10 + y}{2 + y} y = - \frac{3 + 65}{2}

Calculate

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{x = \frac{17 + 65}{1 + 65} y = \frac{- 3 + 65}{2} \cup {x = \frac{17 - 65}{1 - 65} y = - \frac{3 + 65}{2}

Check the solution

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{x = \frac{17 + 65}{1 + 65} y = \frac{- 3 + 65}{2} \cup {x = \frac{17 - 65}{1 - 65} y = - \frac{3 + 65}{2}

Check the solution

More Steps

{x = \frac{17 + 65}{1 + 65} y = \frac{- 3 + 65}{2} \cup {x = \frac{17 - 65}{1 - 65} y = - \frac{3 + 65}{2}

Solution

(x_{1}, y_{1}) = (\frac{17 + 65}{1 + 65}, \frac{- 3 + 65}{2}) (x_{2}, y_{2}) = (\frac{17 - 65}{1 - 65}, - \frac{3 + 65}{2})

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