Question
Solve the system of equations
(a,b,x)=(−113b+1b,b,−5(113b+1)114b2),b∈R
Alternative Form
Infinitely many solutions
Evaluate
{x×5=114ab114ab=ab−(a+b)
Use the commutative property to reorder the terms
{5x=114ab114ab=ab−(a+b)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
{5x=114ab114ab=ab−a−b
Solve the equation for x
More Steps

Evaluate
5x=114ab
Divide both sides
55x=5114ab
Divide the numbers
x=5114ab
{x=5114ab114ab=ab−a−b
Substitute the given value of x into the equation 114ab=ab−a−b
114ab=ab−a−b
Evaluate
114ba=ba−a−b
Collect like terms by calculating the sum or difference of their coefficients
114ba=(b−1)a−b
Move the variable to the left side
114ba−(b−1)a=−b
Subtract the terms
More Steps

Evaluate
114ba−(b−1)a
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
114ba+(−b+1)a
Collect like terms by calculating the sum or difference of their coefficients
(114b−b+1)a
Subtract the terms
More Steps

Evaluate
114b−b
Factor the expression
(114−1)b
Subtract the terms
113b
(113b+1)a
(113b+1)a=−b
Divide both sides
113b+1(113b+1)a=113b+1−b
Divide the numbers
a=113b+1−b
Use b−a=−ba=−ba to rewrite the fraction
a=−113b+1b
Substitute the given value of a into the equation x=5114ab
x=5114(−113b+1b)b
Simplify the expression
x=−5(113b+1)114b2
Solution
(a,b,x)=(−113b+1b,b,−5(113b+1)114b2),b∈R
Alternative Form
Infinitely many solutions
Show Solution
