Question
Solve the system of equations
(a1,b1)=(−30112,−32)(a2,b2)=(30112,32)
Evaluate
{ab=18a÷b18a÷b=11÷5
Calculate
{ab=b18a18a÷b=11÷5
Calculate
More Steps

Evaluate
18a÷b=11÷5
Rewrite the expression
b18a=11÷5
Divide the numbers
b18a=2.2
{ab=b18ab18a=2.2
Solve the equation
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Evaluate
ab=b18a
Cross multiply
ab×b=18a
Simplify the equation
ab2=18a
Move the expression to the left side
ab2−18a=0
Factor the expression
a(b2−18)=0
Separate the equation into 2 possible cases
a=0∪b2−18=0
Solve the equation
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Evaluate
b2−18=0
Move the constant to the right-hand side and change its sign
b2=0+18
Removing 0 doesn't change the value,so remove it from the expression
b2=18
Take the root of both sides of the equation and remember to use both positive and negative roots
b=±18
Simplify the expression
b=±32
Separate the equation into 2 possible cases
b=32∪b=−32
a=0∪b=32∪b=−32
{a=0∪b=32∪b=−32b18a=2.2
Evaluate
{a=0b18a=2.2∪{b=32b18a=2.2∪{b=−32b18a=2.2
Calculate
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Evaluate
{a=0b18a=2.2
Substitute the given value of a into the equation b18a=2.2
b18×0=2.2
Simplify
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Evaluate
b18×0
Any expression multiplied by 0 equals 0
b0
Divide the terms
0
0=2.2
Calculate
{a∈∅b∈∅
{a∈∅b∈∅∪{b=32b18a=2.2∪{b=−32b18a=2.2
Calculate
More Steps

Evaluate
{b=32b18a=2.2
Substitute the given value of b into the equation b18a=2.2
3218a=2.2
Cancel out the common factor 3
26a=2.2
Convert the expressions
26a=511
Multiply both sides of the equation by 2
26a×2=5112
Multiply the terms
6a=5112
Multiply by the reciprocal
6a×61=5112×61
Multiply
a=5112×61
Multiply
More Steps

Evaluate
5112×61
To multiply the fractions,multiply the numerators and denominators separately
5×6112
Multiply the numbers
30112
a=30112
Calculate
{a=30112b=32
{a∈∅b∈∅∪{a=30112b=32∪{b=−32b18a=2.2
Calculate
More Steps

Evaluate
{b=−32b18a=2.2
Substitute the given value of b into the equation b18a=2.2
−3218a=2.2
Divide the terms
−26a=2.2
Convert the expressions
−26a=511
Rewrite the expression
2−6a=511
Multiply both sides of the equation by 2
2−6a×2=5112
Multiply the terms
−6a=5112
Change the signs on both sides of the equation
6a=−5112
Multiply by the reciprocal
6a×61=−5112×61
Multiply
a=−5112×61
Multiply
More Steps

Evaluate
−5112×61
To multiply the fractions,multiply the numerators and denominators separately
−5×6112
Multiply the numbers
−30112
a=−30112
Calculate
{a=−30112b=−32
{a∈∅b∈∅∪{a=30112b=32∪{a=−30112b=−32
Rearrange the terms
{a=−30112b=−32∪{a=30112b=32
Check the solution
More Steps

Check the solution
⎩⎨⎧−30112(−32)=18(−30112)÷(−32)18(−30112)÷(−32)=11÷5
Simplify
{2.2=2.22.2=2.2
Evaluate
true
{a=−30112b=−32∪{a=30112b=32
Check the solution
More Steps

Check the solution
{30112×32=18×30112÷3218×30112÷32=11÷5
Simplify
{2.2=2.22.2=2.2
Evaluate
true
{a=−30112b=−32∪{a=30112b=32
Solution
(a1,b1)=(−30112,−32)(a2,b2)=(30112,32)
Show Solution
