Question
Solve the system of equations
(Q,R,a,b,o,u)=(−3abu+3au+3bu−3uai,oua5,a,b,o,u),(u,o,a,b)∈R4
Alternative Form
Infinitely many solutions
Evaluate
{Ruo×3a=155a=15Qiu(a−1)(b−1)
Use the commutative property to reorder the terms
{3Ruoa=155a=15Qiu(a−1)(b−1)
Calculate
{3Ruoa=155a=15iQu(a−1)(b−1)
Solve the equation for Q
More Steps

Evaluate
5a=15iQu(a−1)(b−1)
Evaluate
5a=(15aub−15au−15ub+15u)iQ
Swap the sides of the equation
(15aub−15au−15ub+15u)iQ=5a
Divide both sides
(15aub−15au−15ub+15u)i(15aub−15au−15ub+15u)iQ=(15aub−15au−15ub+15u)i5a
Divide the numbers
Q=(15aub−15au−15ub+15u)i5a
Divide the numbers
More Steps

Evaluate
(15aub−15au−15ub+15u)i5a
Multiply by the Conjugate
(15aub−15au−15ub+15u)i×i5ai
Calculate
−15aub+15au+15ub−15u5ai
Reduce the fraction
−3abu+3au+3bu−3uai
Q=−3abu+3au+3bu−3uai
{3Ruoa=15Q=−3abu+3au+3bu−3uai
Substitute the given value of Q into the equation 3Ruoa=15
3Ruoa=15
Evaluate
3uoaR=15
Divide both sides
3uoa3uoaR=3uoa15
Divide the numbers
R=3uoa15
Divide the numbers
More Steps

Evaluate
3uoa15
Cancel out the common factor 3
uoa5
Calculate
oua5
R=oua5
Solution
(Q,R,a,b,o,u)=(−3abu+3au+3bu−3uai,oua5,a,b,o,u),(u,o,a,b)∈R4
Alternative Form
Infinitely many solutions
Show Solution
