Algebra
Calculus
Trigonometry
Matrix
Question
Solve the system of equations
(x1,y1)=(67+4534,−268+44534)(x2,y2)=(67−4534,−268−44534)
Evaluate
{4x−1×y=536xy=180
Any expression multiplied by 1 remains the same
{4x−y=536xy=180
Solve the equation for y
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Evaluate
4x−y=536
Move the expression to the right-hand side and change its sign
−y=536−4x
Change the signs on both sides of the equation
y=−536+4x
{y=−536+4xxy=180
Substitute the given value of y into the equation xy=180
x(−536+4x)=180
Expand the expression
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Evaluate
x(−536+4x)
Apply the distributive property
x(−536)+x×4x
Use the commutative property to reorder the terms
−536x+x×4x
Multiply the terms
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Evaluate
x×4x
Use the commutative property to reorder the terms
4x×x
Multiply the terms
4x2
−536x+4x2
−536x+4x2=180
Move the expression to the left side
−536x+4x2−180=0
Rewrite in standard form
4x2−536x−180=0
Substitute a=4,b=−536 and c=−180 into the quadratic formula x=2a−b±b2−4ac
x=2×4536±(−536)2−4×4(−180)
Simplify the expression
x=8536±(−536)2−4×4(−180)
Simplify the expression
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Evaluate
(−536)2−4×4(−180)
Multiply
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Multiply the terms
4×4(−180)
Rewrite the expression
−4×4×180
Multiply the terms
−2880
(−536)2−(−2880)
Rewrite the expression
5362−(−2880)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
5362+2880
x=8536±5362+2880
Simplify the radical expression
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Evaluate
5362+2880
Add the numbers
290176
Write the expression as a product where the root of one of the factors can be evaluated
64×4534
Write the number in exponential form with the base of 8
82×4534
The root of a product is equal to the product of the roots of each factor
82×4534
Reduce the index of the radical and exponent with 2
84534
x=8536±84534
Separate the equation into 2 possible cases
x=8536+84534x=8536−84534
Simplify the expression
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Evaluate
x=8536+84534
Divide the terms
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Evaluate
8536+84534
Rewrite the expression
88(67+4534)
Reduce the fraction
67+4534
x=67+4534
x=67+4534x=8536−84534
Simplify the expression
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Evaluate
x=8536−84534
Divide the terms
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Evaluate
8536−84534
Rewrite the expression
88(67−4534)
Reduce the fraction
67−4534
x=67−4534
x=67+4534x=67−4534
Evaluate the logic
x=67+4534∪x=67−4534
Rearrange the terms
{x=67+4534y=−536+4x∪{x=67−4534y=−536+4x
Calculate
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Evaluate
{x=67+4534y=−536+4x
Substitute the given value of x into the equation y=−536+4x
y=−536+4(67+4534)
Calculate
y=−268+44534
Calculate
{x=67+4534y=−268+44534
{x=67+4534y=−268+44534∪{x=67−4534y=−536+4x
Calculate
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Evaluate
{x=67−4534y=−536+4x
Substitute the given value of x into the equation y=−536+4x
y=−536+4(67−4534)
Calculate
y=−268−44534
Calculate
{x=67−4534y=−268−44534
{x=67+4534y=−268+44534∪{x=67−4534y=−268−44534
Check the solution
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Check the solution
⎩⎨⎧4(67+4534)−1×(−268+44534)=536(67+4534)(−268+44534)=180
Simplify
{536=536180=180
Evaluate
true
{x=67+4534y=−268+44534∪{x=67−4534y=−268−44534
Check the solution
More Steps
Check the solution
⎩⎨⎧4(67−4534)−1×(−268−44534)=536(67−4534)(−268−44534)=180
Simplify
{536=536180=180
Evaluate
true
{x=67+4534y=−268+44534∪{x=67−4534y=−268−44534
Solution
(x1,y1)=(67+4534,−268+44534)(x2,y2)=(67−4534,−268−44534)
Show Solution
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