Question
Solve the system of equations
Solve using the substitution method
Solve using the elimination method
(ξ,d)=(9e2,23e)
Alternative Form
(ξ,d)≈(0.081751,4.077423)
Evaluate
{eξ=32dξ32dξ=92
Solve the equation
More Steps

Evaluate
eξ=32dξ
Move the expression to the left side
eξ−32dξ=0
Factor the expression
ξ(e−32d)=0
Separate the equation into 2 possible cases
ξ=0∪e−32d=0
Solve the equation
More Steps

Evaluate
e−32d=0
Move the constant to the right-hand side and change its sign
−32d=0−e
Removing 0 doesn't change the value,so remove it from the expression
−32d=−e
Change the signs on both sides of the equation
32d=e
Multiply by the reciprocal
32d×23=e×23
Multiply
d=e×23
Multiply
d=23e
ξ=0∪d=23e
{ξ=0∪d=23e32dξ=92
Evaluate
{ξ=032dξ=92∪{d=23e32dξ=92
Calculate
More Steps

Evaluate
{ξ=032dξ=92
Substitute the given value of ξ into the equation 32dξ=92
32d×0=92
Any expression multiplied by 0 equals 0
0=92
Calculate
{ξ∈∅d∈∅
{ξ∈∅d∈∅∪{d=23e32dξ=92
Calculate
More Steps

Evaluate
{d=23e32dξ=92
Substitute the given value of d into the equation 32dξ=92
32×23eξ=92
Multiply the terms
eξ=92
Multiply by the reciprocal
eξ×e1=92×e1
Multiply
ξ=92×e1
To multiply the fractions,multiply the numerators and denominators separately
ξ=9e2
Calculate
{ξ=9e2d=23e
{ξ∈∅d∈∅∪{ξ=9e2d=23e
Rearrange the terms
{ξ=9e2d=23e
Check the solution
More Steps

Check the solution
{e×9e2=32×23e×9e232×23e×9e2=92
Simplify
{0.2˙=0.2˙0.2˙=0.2˙
Evaluate
true
{ξ=9e2d=23e
Solution
(ξ,d)=(9e2,23e)
Alternative Form
(ξ,d)≈(0.081751,4.077423)
Show Solution
