Question
Solve the system of equations
κ∈∅
Alternative Form
No solution
Evaluate
⎩⎨⎧κ×1=4κ×24κ×2=74κ×3κ×474κ×3κ×4=1756
Calculate
More Steps

Evaluate
κ×1=4κ×2
Any expression multiplied by 1 remains the same
κ=4κ×2
Multiply the terms
κ=8κ
Add or subtract both sides
κ−8κ=0
Subtract the terms
More Steps

Evaluate
κ−8κ
Collect like terms by calculating the sum or difference of their coefficients
(1−8)κ
Subtract the numbers
−7κ
−7κ=0
Change the signs on both sides of the equation
7κ=0
Rewrite the expression
κ=0
⎩⎨⎧κ=04κ×2=74κ×3κ×474κ×3κ×4=1756
Calculate
⎩⎨⎧κ=0κ×2=74κ×3κ74κ×3κ×4=1756
Calculate
More Steps

Evaluate
κ×2=74κ×3κ
Use the commutative property to reorder the terms
2κ=74κ×3κ
Multiply
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Evaluate
74κ×3κ
Multiply the terms
712κ×κ
Multiply the terms
712κ2
2κ=712κ2
Add or subtract both sides
2κ−712κ2=0
Factor the expression
More Steps

Evaluate
2κ−712κ2
Rewrite the expression
72κ×7−72κ×6κ
Factor out 72κ from the expression
72κ(7−6κ)
72κ(7−6κ)=0
When the product of factors equals 0,at least one factor is 0
72κ=07−6κ=0
Solve the equation for κ
κ=07−6κ=0
Solve the equation for κ
More Steps

Evaluate
7−6κ=0
Move the constant to the right-hand side and change its sign
−6κ=0−7
Removing 0 doesn't change the value,so remove it from the expression
−6κ=−7
Change the signs on both sides of the equation
6κ=7
Divide both sides
66κ=67
Divide the numbers
κ=67
κ=0κ=67
Calculate
κ=0∪κ=67
⎩⎨⎧κ=0κ=0∪κ=6774κ×3κ×4=1756
Calculate
More Steps

Evaluate
74κ×3κ×4=1756
Multiply
More Steps

Evaluate
74κ×3κ×4
Multiply the terms
748κ×κ
Multiply the terms
748κ2
748κ2=1756
Multiply by the reciprocal
748κ2×487=1756×487
Multiply
κ2=1756×487
Multiply
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Evaluate
1756×487
Reduce the numbers
1751×87
Reduce the numbers
251×81
To multiply the fractions,multiply the numerators and denominators separately
25×81
Multiply the numbers
2001
κ2=2001
Take the root of both sides of the equation and remember to use both positive and negative roots
κ=±2001
Simplify the expression
More Steps

Evaluate
2001
To take a root of a fraction,take the root of the numerator and denominator separately
2001
Simplify the radical expression
2001
Simplify the radical expression
1021
Multiply by the Conjugate
102×22
Multiply the numbers
202
κ=±202
Separate the equation into 2 possible cases
κ=202∪κ=−202
⎩⎨⎧κ=0κ=0∪κ=67κ=202∪κ=−202
Solution
κ∈∅
Alternative Form
No solution
Show Solution
