Algebra
Calculus
Trigonometry
Matrix
Question
Solve the system of equations
(x1,y1)=(101+21,2−5+521)(x2,y2)=(101−21,−25+521)
Evaluate
{xy=25x−y25x−y=5
Solve the equation for y
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Evaluate
25x−y=5
Move the expression to the right-hand side and change its sign
−y=5−25x
Change the signs on both sides of the equation
y=−5+25x
{xy=25x−yy=−5+25x
Substitute the given value of y into the equation xy=25x−y
x(−5+25x)=25x−(−5+25x)
Simplify
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Evaluate
25x−(−5+25x)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
25x+5−25x
The sum of two opposites equals 0
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Evaluate
25x−25x
Collect like terms
(25−25)x
Add the coefficients
0×x
Calculate
0
0+5
Remove 0
5
x(−5+25x)=5
Expand the expression
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Evaluate
x(−5+25x)
Apply the distributive property
x(−5)+x×25x
Use the commutative property to reorder the terms
−5x+x×25x
Multiply the terms
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Evaluate
x×25x
Use the commutative property to reorder the terms
25x×x
Multiply the terms
25x2
−5x+25x2
−5x+25x2=5
Move the expression to the left side
−5x+25x2−5=0
Rewrite in standard form
25x2−5x−5=0
Substitute a=25,b=−5 and c=−5 into the quadratic formula x=2a−b±b2−4ac
x=2×255±(−5)2−4×25(−5)
Simplify the expression
x=505±(−5)2−4×25(−5)
Simplify the expression
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Evaluate
(−5)2−4×25(−5)
Multiply
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Multiply the terms
4×25(−5)
Rewrite the expression
−4×25×5
Multiply the terms
−500
(−5)2−(−500)
Rewrite the expression
52−(−500)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
52+500
Evaluate the power
25+500
Add the numbers
525
x=505±525
Simplify the radical expression
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Evaluate
525
Write the expression as a product where the root of one of the factors can be evaluated
25×21
Write the number in exponential form with the base of 5
52×21
The root of a product is equal to the product of the roots of each factor
52×21
Reduce the index of the radical and exponent with 2
521
x=505±521
Separate the equation into 2 possible cases
x=505+521x=505−521
Simplify the expression
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Evaluate
x=505+521
Divide the terms
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Evaluate
505+521
Rewrite the expression
505(1+21)
Cancel out the common factor 5
101+21
x=101+21
x=101+21x=505−521
Simplify the expression
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Evaluate
x=505−521
Divide the terms
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Evaluate
505−521
Rewrite the expression
505(1−21)
Cancel out the common factor 5
101−21
x=101−21
x=101+21x=101−21
Evaluate the logic
x=101+21∪x=101−21
Rearrange the terms
{x=101+21y=−5+25x∪{x=101−21y=−5+25x
Calculate
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Evaluate
{x=101+21y=−5+25x
Substitute the given value of x into the equation y=−5+25x
y=−5+25×101+21
Calculate
y=2−5+521
Calculate
{x=101+21y=2−5+521
{x=101+21y=2−5+521∪{x=101−21y=−5+25x
Calculate
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Evaluate
{x=101−21y=−5+25x
Substitute the given value of x into the equation y=−5+25x
y=−5+25×101−21
Calculate
y=−25+521
Calculate
{x=101−21y=−25+521
{x=101+21y=2−5+521∪{x=101−21y=−25+521
Check the solution
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Check the solution
{101+21×2−5+521=25×101+21−2−5+52125×101+21−2−5+521=5
Simplify
{5=55=5
Evaluate
true
{x=101+21y=2−5+521∪{x=101−21y=−25+521
Check the solution
More Steps
Check the solution
⎩⎨⎧101−21×(−25+521)=25×101−21−(−25+521)25×101−21−(−25+521)=5
Simplify
{5=55=5
Evaluate
true
{x=101+21y=2−5+521∪{x=101−21y=−25+521
Solution
(x1,y1)=(101+21,2−5+521)(x2,y2)=(101−21,−25+521)
Show Solution
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