Solve x y=0 -3x-3y=-1

Question

Solve the system of equations

(x_{1}, y_{1}) = (\frac{1 + 37}{6}, \frac{1 - 37}{6}) (x_{2}, y_{2}) = (\frac{1 - 37}{6}, \frac{1 + 37}{6})

Evaluate

{x y = 0 - 3 x - 3 y 0 - 3 x - 3 y = - 1

Removing 0 doesn't change the value,so remove it from the expression

{x y = - 3 x - 3 y 0 - 3 x - 3 y = - 1

Removing 0 doesn't change the value,so remove it from the expression

{x y = - 3 x - 3 y - 3 x - 3 y = - 1

Solve the equation for x

More Steps

{x y = - 3 x - 3 y x = \frac{1 - 3 y}{3}

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

\frac{1 - 3 y}{3} \times y = - 3 \times \frac{1 - 3 y}{3} - 3 y

Simplify

More Steps

\frac{y ( 1 - 3 y )}{3} = - 3 \times \frac{1 - 3 y}{3} - 3 y

Simplify

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\frac{y ( 1 - 3 y )}{3} = - 1

Cross multiply

y (1 - 3 y) = 3 (- 1)

Simplify the equation

y (1 - 3 y) = - 3

Expand the expression

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y - 3 y^{2} = - 3

Move the expression to the left side

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

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

Rewrite in standard form

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

Multiply both sides

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

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

y = \frac{1 \pm ( - 1 ) ^{2} - 4 \times 3 ( - 3 )}{2 \times 3}

Simplify the expression

y = \frac{1 \pm ( - 1 ) ^{2} - 4 \times 3 ( - 3 )}{6}

Simplify the expression

More Steps

y = \frac{1 \pm 37}{6}

Separate the equation into 2 possible cases

y = \frac{1 + 37}{6} y = \frac{1 - 37}{6}

Evaluate the logic

y = \frac{1 + 37}{6} \cup y = \frac{1 - 37}{6}

Rearrange the terms

{x = \frac{1 - 3 y}{3} y = \frac{1 + 37}{6} \cup {x = \frac{1 - 3 y}{3} y = \frac{1 - 37}{6}

Calculate

More Steps

{x = \frac{1 - 37}{6} y = \frac{1 + 37}{6} \cup {x = \frac{1 - 3 y}{3} y = \frac{1 - 37}{6}

Calculate

More Steps

{x = \frac{1 - 37}{6} y = \frac{1 + 37}{6} \cup {x = \frac{1 + 37}{6} y = \frac{1 - 37}{6}

Calculate

{x = \frac{1 + 37}{6} y = \frac{1 - 37}{6} \cup {x = \frac{1 - 37}{6} y = \frac{1 + 37}{6}

Check the solution

More Steps

{x = \frac{1 + 37}{6} y = \frac{1 - 37}{6} \cup {x = \frac{1 - 37}{6} y = \frac{1 + 37}{6}

Check the solution

More Steps

{x = \frac{1 + 37}{6} y = \frac{1 - 37}{6} \cup {x = \frac{1 - 37}{6} y = \frac{1 + 37}{6}

Solution

(x_{1}, y_{1}) = (\frac{1 + 37}{6}, \frac{1 - 37}{6}) (x_{2}, y_{2}) = (\frac{1 - 37}{6}, \frac{1 + 37}{6})

Show Solution

Solve the system of equations

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