Algebra
Calculus
Trigonometry
Matrix
Question
Solve the system of equations
(x1,y1)=(96887+17609,2−87+17609)(x2,y2)=(96887−17609,−287+17609)
Evaluate
{xy=484x−y484x−y=87
Solve the equation for y
More Steps
Evaluate
484x−y=87
Move the expression to the right-hand side and change its sign
−y=87−484x
Change the signs on both sides of the equation
y=−87+484x
{xy=484x−yy=−87+484x
Substitute the given value of y into the equation xy=484x−y
x(−87+484x)=484x−(−87+484x)
Simplify
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Evaluate
484x−(−87+484x)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
484x+87−484x
The sum of two opposites equals 0
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Evaluate
484x−484x
Collect like terms
(484−484)x
Add the coefficients
0×x
Calculate
0
0+87
Remove 0
87
x(−87+484x)=87
Expand the expression
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Evaluate
x(−87+484x)
Apply the distributive property
x(−87)+x×484x
Use the commutative property to reorder the terms
−87x+x×484x
Multiply the terms
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Evaluate
x×484x
Use the commutative property to reorder the terms
484x×x
Multiply the terms
484x2
−87x+484x2
−87x+484x2=87
Move the expression to the left side
−87x+484x2−87=0
Rewrite in standard form
484x2−87x−87=0
Substitute a=484,b=−87 and c=−87 into the quadratic formula x=2a−b±b2−4ac
x=2×48487±(−87)2−4×484(−87)
Simplify the expression
x=96887±(−87)2−4×484(−87)
Simplify the expression
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Evaluate
(−87)2−4×484(−87)
Multiply
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Multiply the terms
4×484(−87)
Rewrite the expression
−4×484×87
Multiply the terms
−168432
(−87)2−(−168432)
Rewrite the expression
872−(−168432)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
872+168432
Evaluate the power
7569+168432
Add the numbers
176001
x=96887±176001
Simplify the radical expression
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Evaluate
176001
Write the expression as a product where the root of one of the factors can be evaluated
289×609
Write the number in exponential form with the base of 17
172×609
The root of a product is equal to the product of the roots of each factor
172×609
Reduce the index of the radical and exponent with 2
17609
x=96887±17609
Separate the equation into 2 possible cases
x=96887+17609x=96887−17609
Evaluate the logic
x=96887+17609∪x=96887−17609
Rearrange the terms
{x=96887+17609y=−87+484x∪{x=96887−17609y=−87+484x
Calculate
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Evaluate
{x=96887+17609y=−87+484x
Substitute the given value of x into the equation y=−87+484x
y=−87+484×96887+17609
Calculate
y=2−87+17609
Calculate
{x=96887+17609y=2−87+17609
{x=96887+17609y=2−87+17609∪{x=96887−17609y=−87+484x
Calculate
More Steps
Evaluate
{x=96887−17609y=−87+484x
Substitute the given value of x into the equation y=−87+484x
y=−87+484×96887−17609
Calculate
y=−287+17609
Calculate
{x=96887−17609y=−287+17609
{x=96887+17609y=2−87+17609∪{x=96887−17609y=−287+17609
Check the solution
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Check the solution
{96887+17609×2−87+17609=484×96887+17609−2−87+17609484×96887+17609−2−87+17609=87
Simplify
{87=8787=87
Evaluate
true
{x=96887+17609y=2−87+17609∪{x=96887−17609y=−287+17609
Check the solution
More Steps
Check the solution
⎩⎨⎧96887−17609×(−287+17609)=484×96887−17609−(−287+17609)484×96887−17609−(−287+17609)=87
Simplify
{87=8787=87
Evaluate
true
{x=96887+17609y=2−87+17609∪{x=96887−17609y=−287+17609
Solution
(x1,y1)=(96887+17609,2−87+17609)(x2,y2)=(96887−17609,−287+17609)
Show Solution
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