Question
Solve the system of equations
(w,x)∈∅
Alternative Form
No solution
Evaluate
⎩⎨⎧x2=3wx23wx2=5wx25wx2=169
Solve the equation
More Steps

Evaluate
x2=3wx2
Move the expression to the left side
x2−3wx2=0
Factor the expression
x2(1−3w)=0
Separate the equation into 2 possible cases
x2=0∪1−3w=0
The only way a power can be 0 is when the base equals 0
x=0∪1−3w=0
Solve the equation
More Steps

Evaluate
1−3w=0
Move the constant to the right-hand side and change its sign
−3w=0−1
Removing 0 doesn't change the value,so remove it from the expression
−3w=−1
Change the signs on both sides of the equation
3w=1
Divide both sides
33w=31
Divide the numbers
w=31
x=0∪w=31
Find the union
w=31∪x=0
⎩⎨⎧x=0∪w=313wx2=5wx25wx2=169
Evaluate
⎩⎨⎧x=03wx2=5wx25wx2=169∪⎩⎨⎧w=313wx2=5wx25wx2=169
Calculate
More Steps

Evaluate
⎩⎨⎧x=03wx2=5wx25wx2=169
Substitute the given value of x into the equation {3wx2=5wx25wx2=169
{3w×02=5w×025w×02=169
Simplify
More Steps

Evaluate
3w×02=5w×02
Simplify
0=5w×02
Simplify
0=0
{0=05w×02=169
Simplify
{0=00=169
Simplify the expression
0=169
Calculate
{w∈∅x∈∅
{w∈∅x∈∅∪⎩⎨⎧w=313wx2=5wx25wx2=169
Calculate
More Steps

Evaluate
⎩⎨⎧w=313wx2=5wx25wx2=169
Substitute the given value of w into the equation {3wx2=5wx25wx2=169
{3×31x2=5×31x25×31x2=169
Simplify
More Steps

Evaluate
3×31x2=5×31x2
Simplify
x2=5×31x2
Multiply the numbers
x2=35x2
{x2=35x25×31x2=169
Multiply the numbers
{x2=35x235x2=169
Solve the equation for x
More Steps

Evaluate
x2=35x2
Move the expression to the left side
x2−35x2=0
Add or subtract both sides
−32x2=0
Change the signs on both sides of the equation
32x2=0
Rewrite the expression
x2=0
The only way a power can be 0 is when the base equals 0
x=0
{x=035x2=169
Substitute the given value of x into the equation 35x2=169
35×02=169
Simplify
More Steps

Evaluate
35×02
Calculate
35×0
Any expression multiplied by 0 equals 0
0
0=169
Calculate
{w∈∅x∈∅
{w∈∅x∈∅∪{w∈∅x∈∅
Rearrange the terms
{w∈∅x∈∅
Solution
(w,x)∈∅
Alternative Form
No solution
Show Solution
