Solve 2x 9y=-144x-3y=-7

Question

Solve the system of equations

(x_{1}, y_{1}) = (\frac{7 + 721}{288}, \frac{7 - 721}{6}) (x_{2}, y_{2}) = (\frac{7 - 721}{288}, \frac{7 + 721}{6})

Evaluate

{2 x \times 9 y = - 144 x - 3 y - 144 x - 3 y = - 7

Calculate

{18 x y = - 144 x - 3 y - 144 x - 3 y = - 7

Solve the equation for x

More Steps

{18 x y = - 144 x - 3 y x = \frac{7 - 3 y}{144}

Substitute the given value of x into the equation 18 x y = - 144 x - 3 y

18 \times \frac{7 - 3 y}{144} \times y = - 144 \times \frac{7 - 3 y}{144} - 3 y

Simplify

More Steps

\frac{y ( 7 - 3 y )}{8} = - 144 \times \frac{7 - 3 y}{144} - 3 y

Simplify

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\frac{y ( 7 - 3 y )}{8} = - 7

Cross multiply

y (7 - 3 y) = 8 (- 7)

Simplify the equation

y (7 - 3 y) = - 56

Expand the expression

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7 y - 3 y^{2} = - 56

Move the expression to the left side

7 y - 3 y^{2} - (- 56) = 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 - 3 y^{2} + 56 = 0

Rewrite in standard form

- 3 y^{2} + 7 y + 56 = 0

Multiply both sides

3 y^{2} - 7 y - 56 = 0

Substitute a= 3,b= - 7 and c= - 56 into the quadratic formula y = \frac{- b \pm b ^{2} - 4 a c}{2 a}

y = \frac{7 \pm ( - 7 ) ^{2} - 4 \times 3 ( - 56 )}{2 \times 3}

Simplify the expression

y = \frac{7 \pm ( - 7 ) ^{2} - 4 \times 3 ( - 56 )}{6}

Simplify the expression

More Steps

y = \frac{7 \pm 721}{6}

Separate the equation into 2 possible cases

y = \frac{7 + 721}{6} y = \frac{7 - 721}{6}

Evaluate the logic

y = \frac{7 + 721}{6} \cup y = \frac{7 - 721}{6}

Rearrange the terms

{x = \frac{7 - 3 y}{144} y = \frac{7 + 721}{6} \cup {x = \frac{7 - 3 y}{144} y = \frac{7 - 721}{6}

Calculate

More Steps

{x = \frac{7 - 721}{288} y = \frac{7 + 721}{6} \cup {x = \frac{7 - 3 y}{144} y = \frac{7 - 721}{6}

Calculate

More Steps

{x = \frac{7 - 721}{288} y = \frac{7 + 721}{6} \cup {x = \frac{7 + 721}{288} y = \frac{7 - 721}{6}

Calculate

{x = \frac{7 + 721}{288} y = \frac{7 - 721}{6} \cup {x = \frac{7 - 721}{288} y = \frac{7 + 721}{6}

Check the solution

More Steps

{x = \frac{7 + 721}{288} y = \frac{7 - 721}{6} \cup {x = \frac{7 - 721}{288} y = \frac{7 + 721}{6}

Check the solution

More Steps

{x = \frac{7 + 721}{288} y = \frac{7 - 721}{6} \cup {x = \frac{7 - 721}{288} y = \frac{7 + 721}{6}

Solution

(x_{1}, y_{1}) = (\frac{7 + 721}{288}, \frac{7 - 721}{6}) (x_{2}, y_{2}) = (\frac{7 - 721}{288}, \frac{7 + 721}{6})

Show Solution

Solve the system of equations

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