Solve 13=-9y-11x,4=5x-2y

Question

Solve the system of equations

Solve using the substitution method

Solve using the elimination method

Solve using the Gauss-Jordan method

(x, y) = (\frac{10}{67}, - \frac{109}{67})

Alternative Form

(x, y) \approx (0.149254, - 1.626866)

Evaluate

{13 = - 9 y - 11 x 4 = 5 x - 2 y

Solve the equation for x

More Steps

{x = - \frac{13 + 9 y}{11} 4 = 5 x - 2 y

Substitute the given value of x into the equation 4 = 5 x - 2 y

4 = 5 (- \frac{13 + 9 y}{11}) - 2 y

Multiply the terms

More Steps

4 = - \frac{5 ( 13 + 9 y )}{11} - 2 y

Swap the sides of the equation

- \frac{5 ( 13 + 9 y )}{11} - 2 y = 4

Multiply both sides of the equation by LCD

(- \frac{5 ( 13 + 9 y )}{11} - 2 y) \times 11 = 4 \times 11

Simplify the equation

More Steps

- 65 - 67 y = 4 \times 11

Simplify the equation

- 65 - 67 y = 44

Move the constant to the right side

- 67 y = 44 + 65

Add the numbers

- 67 y = 109

Change the signs on both sides of the equation

67 y = - 109

Divide both sides

\frac{67 y}{67} = \frac{- 109}{67}

Divide the numbers

y = \frac{- 109}{67}

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

y = - \frac{109}{67}

Substitute the given value of y into the equation x = - \frac{13 + 9 y}{11}

x = - \frac{13 + 9 ( - \frac{109}{67} )}{11}

Simplify the expression

x = \frac{- 13 + 9 \times \frac{109}{67}}{11}

Calculate

x = \frac{10}{67}

Calculate

{x = \frac{10}{67} y = - \frac{109}{67}

Check the solution

More Steps

{x = \frac{10}{67} y = - \frac{109}{67}

Solution

(x, y) = (\frac{10}{67}, - \frac{109}{67})

Alternative Form

(x, y) \approx (0.149254, - 1.626866)

Show Solution

Neither parallel nor perpendicular

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