Algebra
Calculus
Trigonometry
Matrix
Question
Solve the system of equations
(x1,y1)=(90+3905,−360+12905)(x2,y2)=(90−3905,−360−12905)
Evaluate
{4x−1×y=720xy=180
Any expression multiplied by 1 remains the same
{4x−y=720xy=180
Solve the equation for y
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Evaluate
4x−y=720
Move the expression to the right-hand side and change its sign
−y=720−4x
Change the signs on both sides of the equation
y=−720+4x
{y=−720+4xxy=180
Substitute the given value of y into the equation xy=180
x(−720+4x)=180
Expand the expression
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Evaluate
x(−720+4x)
Apply the distributive property
x(−720)+x×4x
Use the commutative property to reorder the terms
−720x+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
−720x+4x2
−720x+4x2=180
Move the expression to the left side
−720x+4x2−180=0
Rewrite in standard form
4x2−720x−180=0
Substitute a=4,b=−720 and c=−180 into the quadratic formula x=2a−b±b2−4ac
x=2×4720±(−720)2−4×4(−180)
Simplify the expression
x=8720±(−720)2−4×4(−180)
Simplify the expression
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Evaluate
(−720)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
(−720)2−(−2880)
Rewrite the expression
7202−(−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
7202+2880
x=8720±7202+2880
Simplify the radical expression
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Evaluate
7202+2880
Add the numbers
521280
Write the expression as a product where the root of one of the factors can be evaluated
576×905
Write the number in exponential form with the base of 24
242×905
The root of a product is equal to the product of the roots of each factor
242×905
Reduce the index of the radical and exponent with 2
24905
x=8720±24905
Separate the equation into 2 possible cases
x=8720+24905x=8720−24905
Simplify the expression
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Evaluate
x=8720+24905
Divide the terms
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Evaluate
8720+24905
Rewrite the expression
88(90+3905)
Reduce the fraction
90+3905
x=90+3905
x=90+3905x=8720−24905
Simplify the expression
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Evaluate
x=8720−24905
Divide the terms
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Evaluate
8720−24905
Rewrite the expression
88(90−3905)
Reduce the fraction
90−3905
x=90−3905
x=90+3905x=90−3905
Evaluate the logic
x=90+3905∪x=90−3905
Rearrange the terms
{x=90+3905y=−720+4x∪{x=90−3905y=−720+4x
Calculate
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Evaluate
{x=90+3905y=−720+4x
Substitute the given value of x into the equation y=−720+4x
y=−720+4(90+3905)
Calculate
y=−360+12905
Calculate
{x=90+3905y=−360+12905
{x=90+3905y=−360+12905∪{x=90−3905y=−720+4x
Calculate
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Evaluate
{x=90−3905y=−720+4x
Substitute the given value of x into the equation y=−720+4x
y=−720+4(90−3905)
Calculate
y=−360−12905
Calculate
{x=90−3905y=−360−12905
{x=90+3905y=−360+12905∪{x=90−3905y=−360−12905
Check the solution
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Check the solution
⎩⎨⎧4(90+3905)−1×(−360+12905)=720(90+3905)(−360+12905)=180
Simplify
{720=720180=180
Evaluate
true
{x=90+3905y=−360+12905∪{x=90−3905y=−360−12905
Check the solution
More Steps
Check the solution
⎩⎨⎧4(90−3905)−1×(−360−12905)=720(90−3905)(−360−12905)=180
Simplify
{720=720180=180
Evaluate
true
{x=90+3905y=−360+12905∪{x=90−3905y=−360−12905
Solution
(x1,y1)=(90+3905,−360+12905)(x2,y2)=(90−3905,−360−12905)
Show Solution
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