Algebra
Calculus
Trigonometry
Matrix
Question
Solve the system of equations
(x1,y1)=(16,4)(x2,y2)=(4,16)
Evaluate
{x+y=6xy=8
Find the domain
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Evaluate
⎩⎨⎧x≥0y≥0xy≥0
Separate the inequality into 2 possible cases
⎩⎨⎧x≥0y≥0{x≥0y≥0∪{x≤0y≤0
Find the intersection
{x≥0y≥0
Calculate
x≥0,y≥0
{x+y=6xy=8,x≥0,y≥0
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
Simplify
36y−12yy+y×y
Multiply the terms
36y−12yy+y2
36y−12yy+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
Evaluate
6y=8+y,8+y≥0
Evaluate
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Evaluate
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
6y=8+y,y≥−8
Solve the equation for y
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Evaluate
6y=8+y
Raise both sides of the equation to the 2-th power to eliminate the isolated 2-th root
(6y)2=(8+y)2
Evaluate the power
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
Multiply both sides of the equation by −1
−y(−1)=−4(−1)
Multiply the numbers
−y(−1)=4
Multiply the numbers
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 if the solution is in the defined range
{x=16y=4∪{x=4y=16,x≥0,y≥0
Find the intersection of the solution and the defined range
{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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