Algebra
Calculus
Trigonometry
Matrix
Question
Solve the system of equations
(x1,y1)=(16,4)(x2,y2)=(4,16)
Evaluate
{x+y=6xy=8
Solve the equation for x
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Evaluate
x+y=6
Move the expression to the right-hand side and change its sign
x=6−y
Raise both sides of the equation to the 2-th power to eliminate the isolated 2-th root
(x)2=(6−y)2
Evaluate the power
x=36−12y+y
{x=36−12y+yxy=8
Substitute the given value of x into the equation xy=8
(36−12y+y)y=8
Simplify
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Evaluate
(36−12y+y)y
Multiply the terms
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Evaluate
(36−12y+y)y
Use the the distributive property to expand the expression
36y−12y×y+y×y
Multiply the terms
36y−12y×y+y2
36y−12y×y+y2
Complete the square
(6y−y)2
Reduce the index of the radical and exponent with 2
6y−y
6y−y=8
Move the variable to the right-hand side and change its sign
6y=8+y
Rewrite the expression
y=68+y
Evaluate
y=68+y,68+y≥0
Evaluate
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Evaluate
68+y≥0
Simplify
8+y≥0
Move the constant to the right side
y≥0−8
Removing 0 doesn't change the value,so remove it from the expression
y≥−8
y=68+y,y≥−8
Solve the equation for y
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Evaluate
y=68+y
Raise both sides of the equation to the 2-th power to eliminate the isolated 2-th root
(y)2=(68+y)2
Evaluate the power
y=3664+16y+y2
Cross multiply
y×36=64+16y+y2
Simplify the equation
36y=64+16y+y2
Move the expression to the left side
36y−(64+16y+y2)=0
Subtract the terms
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Evaluate
36y−(64+16y+y2)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
36y−64−16y−y2
Subtract the terms
20y−64−y2
20y−64−y2=0
Factor the expression
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Evaluate
20y−64−y2
Rewrite the expression
−64+16y+4y−y2
Factor out −16 from the expression
−16(4−y)+4y−y2
Factor out y from the expression
−16(4−y)+y(4−y)
Factor out 4−y from the expression
(−16+y)(4−y)
(−16+y)(4−y)=0
When the product of factors equals 0,at least one factor is 0
−16+y=04−y=0
Solve the equation for y
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Evaluate
−16+y=0
Move the constant to the right-hand side and change its sign
y=0+16
Removing 0 doesn't change the value,so remove it from the expression
y=16
y=164−y=0
Solve the equation for y
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Evaluate
4−y=0
Move the constant to the right-hand side and change its sign
−y=0−4
Removing 0 doesn't change the value,so remove it from the expression
−y=−4
Change the signs on both sides of the equation
y=4
y=16y=4
Calculate
y=16∪y=4
y=16∪y=4,y≥−8
Find the intersection
y=16∪y=4
Rearrange the terms
{x=36−12y+yy=16∪{x=36−12y+yy=4
Calculate
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Evaluate
{x=36−12y+yy=16
Substitute the given value of y into the equation x=36−12y+y
x=36−1216+16
Simplify the expression
x=4
Calculate
{x=4y=16
{x=4y=16∪{x=36−12y+yy=4
Calculate
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Evaluate
{x=36−12y+yy=4
Substitute the given value of y into the equation x=36−12y+y
x=36−124+4
Simplify the expression
x=16
Calculate
{x=16y=4
{x=4y=16∪{x=16y=4
Calculate
{x=16y=4∪{x=4y=16
Check the solution
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Check the solution
{16+4=616×4=8
Simplify
{6=68=8
Evaluate
true
{x=16y=4∪{x=4y=16
Check the solution
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Check the solution
{4+16=64×16=8
Simplify
{6=68=8
Evaluate
true
{x=16y=4∪{x=4y=16
Solution
(x1,y1)=(16,4)(x2,y2)=(4,16)
Show Solution
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