Solve -x y=4 root(2)(2);5x y=2 root(2)(5) - ScanMath

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Type your math problem... -x y=4 root(2)(2);5x y=2 root(2)(5)

Question

Solve the system of equations

(r_{1}, x_{1}, y_{1}) = (0, 0, y), y \in R (r_{2}, x_{2}, y_{2}) = (0, x, 0), x \in R

Evaluate

{- x y = 4 ro \times o t \times 2 \times 2 5 x y = 2 ro \times o t \times 2 \times 5

Calculate

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{- x y = 16 r o^{2} t 5 x y = 2 ro \times o t \times 2 \times 5

Calculate

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{- x y = 16 r o^{2} t 5 x y = 20 r o^{2} t

Solve the equation for r

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{r = - \frac{x y}{16 o ^{2} t} 5 x y = 20 r o^{2} t

Substitute the given value of r into the equation 5 x y = 20 r o^{2} t

5 x y = 20 (- \frac{x y}{16 o ^{2} t}) o^{2} t

Simplify

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5 x y = - \frac{5 x y}{4}

Rewrite the expression

5 x y = \frac{- 5 x y}{4}

Cross multiply

5 x y \times 4 = - 5 x y

Simplify the equation

20 x y = - 5 x y

Move the expression to the left side

20 x y - (- 5 x y) = 0

Subtract the terms

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25 x y = 0

Evaluate

x y = 0

Separate the equation into 2 possible cases

x = 0 y = 0

Solve the equation

x = 0 \cup y = 0

Rearrange the terms

{r = - \frac{x y}{16 o ^{2} t} x = 0 \cup {r = - \frac{x y}{16 o ^{2} t} y = 0

Calculate

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{r = 0 x = 0 \cup {r = - \frac{x y}{16 o ^{2} t} y = 0

Calculate

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{r = 0 x = 0 \cup {r = 0 y = 0

Check the solution

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{r = 0 x = 0 \cup {r = 0 y = 0

Check the solution

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{r = 0 x = 0 \cup {r = 0 y = 0

Solution

(r_{1}, x_{1}, y_{1}) = (0, 0, y), y \in R (r_{2}, x_{2}, y_{2}) = (0, x, 0), x \in R

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