Solve 3x-2y=7 x y=4

Question

Solve the system of equations

Solve using the substitution method

Solve using the elimination method

(x_{1}, y_{1}) = (\frac{14 + 2 91}{21}, \frac{- 7 + 91}{7}) (x_{2}, y_{2}) = (\frac{14 - 2 91}{21}, - \frac{7 + 91}{7})

Evaluate

{3 x - 2 y = 7 x y 7 x y = 4

Solve the equation for x

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{x = \frac{2 y}{3 - 7 y} 7 x y = 4

Substitute the given value of x into the equation 7 x y = 4

7 \times \frac{2 y}{3 - 7 y} \times y = 4

Simplify

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\frac{14 y ^{2}}{3 - 7 y} = 4

Cross multiply

14 y^{2} = (3 - 7 y) \times 4

Simplify the equation

14 y^{2} = 4 (3 - 7 y)

Rewrite the expression

2 \times 7 y^{2} = 2 \times 2 (3 - 7 y)

Evaluate

7 y^{2} = 2 (3 - 7 y)

Expand the expression

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7 y^{2} = 6 - 14 y

Move the expression to the left side

7 y^{2} - (6 - 14 y) = 0

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

7 y^{2} - 6 + 14 y = 0

Rewrite in standard form

7 y^{2} + 14 y - 6 = 0

Substitute a= 7,b= 14 and c= - 6 into the quadratic formula y = \frac{- b \pm b ^{2} - 4 a c}{2 a}

y = \frac{- 14 \pm 1 4 ^{2} - 4 \times 7 ( - 6 )}{2 \times 7}

Simplify the expression

y = \frac{- 14 \pm 1 4 ^{2} - 4 \times 7 ( - 6 )}{14}

Simplify the expression

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y = \frac{- 14 \pm 364}{14}

Simplify the radical expression

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y = \frac{- 14 \pm 2 91}{14}

Separate the equation into 2 possible cases

y = \frac{- 14 + 2 91}{14} y = \frac{- 14 - 2 91}{14}

Simplify the expression

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y = \frac{- 7 + 91}{7} y = \frac{- 14 - 2 91}{14}

Simplify the expression

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y = \frac{- 7 + 91}{7} y = - \frac{7 + 91}{7}

Evaluate the logic

y = \frac{- 7 + 91}{7} \cup y = - \frac{7 + 91}{7}

Rearrange the terms

{x = \frac{2 y}{3 - 7 y} y = \frac{- 7 + 91}{7} \cup {x = \frac{2 y}{3 - 7 y} y = - \frac{7 + 91}{7}

Calculate

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{x = \frac{14 + 2 91}{21} y = \frac{- 7 + 91}{7} \cup {x = \frac{2 y}{3 - 7 y} y = - \frac{7 + 91}{7}

Calculate

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{x = \frac{14 + 2 91}{21} y = \frac{- 7 + 91}{7} \cup {x = \frac{14 - 2 91}{21} y = - \frac{7 + 91}{7}

Check the solution

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{x = \frac{14 + 2 91}{21} y = \frac{- 7 + 91}{7} \cup {x = \frac{14 - 2 91}{21} y = - \frac{7 + 91}{7}

Check the solution

More Steps

{x = \frac{14 + 2 91}{21} y = \frac{- 7 + 91}{7} \cup {x = \frac{14 - 2 91}{21} y = - \frac{7 + 91}{7}

Solution

(x_{1}, y_{1}) = (\frac{14 + 2 91}{21}, \frac{- 7 + 91}{7}) (x_{2}, y_{2}) = (\frac{14 - 2 91}{21}, - \frac{7 + 91}{7})

Show Solution

Solve the system of equations

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