Question
Solve the system of equations
(r1,x1,y1)=(0,0,y),y∈R(r2,x2,y2)=(0,x,0),x∈R
Evaluate
{−xy=4ro×ot×2×25xy=2ro×ot×2×5
Calculate
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Evaluate
4ro×ot×2×2
Multiply the terms
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Evaluate
4×2×2
Multiply the terms
8×2
Multiply the numbers
16
16ro×ot
Multiply the terms
16ro2t
{−xy=16ro2t5xy=2ro×ot×2×5
Calculate
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Evaluate
2ro×ot×2×5
Multiply the terms
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Evaluate
2×2×5
Multiply the terms
4×5
Multiply the numbers
20
20ro×ot
Multiply the terms
20ro2t
{−xy=16ro2t5xy=20ro2t
Solve the equation for r
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Evaluate
−xy=16ro2t
Evaluate
−xy=16o2tr
Swap the sides of the equation
16o2tr=−xy
Divide both sides
16o2t16o2tr=16o2t−xy
Divide the numbers
r=16o2t−xy
Use b−a=−ba=−ba to rewrite the fraction
r=−16o2txy
{r=−16o2txy5xy=20ro2t
Substitute the given value of r into the equation 5xy=20ro2t
5xy=20(−16o2txy)o2t
Simplify
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Evaluate
20(−16o2txy)o2t
Any expression multiplied by 1 remains the same
−20×16o2txy×o2t
Multiply the terms
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Evaluate
20×16o2txy×o2t
Multiply the terms
4o2t5xy×o2t
Multiply the terms
4t5xy×t
Cancel out the common factor t
45xy×1
Multiply the terms
45xy
−45xy
5xy=−45xy
Rewrite the expression
5xy=4−5xy
Cross multiply
5xy×4=−5xy
Simplify the equation
20xy=−5xy
Move the expression to the left side
20xy−(−5xy)=0
Subtract the terms
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Evaluate
20xy−(−5xy)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
20xy+5xy
Collect like terms by calculating the sum or difference of their coefficients
(20+5)xy
Add the numbers
25xy
25xy=0
Evaluate
xy=0
Separate the equation into 2 possible cases
x=0y=0
Solve the equation
x=0∪y=0
Rearrange the terms
{r=−16o2txyx=0∪{r=−16o2txyy=0
Calculate
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Evaluate
{r=−16o2txyx=0
Substitute the given value of x into the equation r=−16o2txy
r=−16o2t0×y
Simplify the expression
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Evaluate
−16o2txy
Substitute back
−16o2t0×y
Any expression multiplied by 0 equals 0
−16o2t0
Divide the terms
−0
Calculate
0
r=0
Calculate
{r=0x=0
{r=0x=0∪{r=−16o2txyy=0
Calculate
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Evaluate
{r=−16o2txyy=0
Substitute the given value of y into the equation r=−16o2txy
r=−16o2tx×0
Simplify the expression
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Evaluate
−16o2txy
Substitute back
−16o2tx×0
Any expression multiplied by 0 equals 0
−16o2t0
Divide the terms
−0
Calculate
0
r=0
Calculate
{r=0y=0
{r=0x=0∪{r=0y=0
Check the solution
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Check the solution
{−0y=4×0×o×ot×2×25×0×y=2×0×o×ot×2×5
Simplify
{0=00=0
Evaluate
true
{r=0x=0∪{r=0y=0
Check the solution
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Check the solution
{−x×0=4×0×o×ot×2×25x×0=2×0×o×ot×2×5
Simplify
{0=00=0
Evaluate
true
{r=0x=0∪{r=0y=0
Solution
(r1,x1,y1)=(0,0,y),y∈R(r2,x2,y2)=(0,x,0),x∈R
Show Solution
