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Solve for [tex]\(x\)[/tex]:
[tex]\[ 3x = 6x - 2 \][/tex]



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[tex]$3 x^2+3 y^2=0$[/tex]
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Response:
[tex]\[ 3x^2 + 3y^2 = 0 \][/tex]



Answer :

GinnyAnswer
Sure, let's go through the steps to solve the equation [tex]\(3x^2 + 3y^2 = 0\)[/tex]:

1. Divide the Equation by 3:
[tex]\[ 3x^2 + 3y^2 = 0 \][/tex]
Dividing both sides of the equation by 3 simplifies the equation:
[tex]\[ x^2 + y^2 = 0 \][/tex]

2. Analyze the Equation [tex]\(x^2 + y^2 = 0\)[/tex]:
Notice that [tex]\(x^2\)[/tex] and [tex]\(y^2\)[/tex] are both squared terms, which means they are both non-negative (i.e., [tex]\(x^2 \geq 0\)[/tex] and [tex]\(y^2 \geq 0\)[/tex]). The sum of two non-negative terms equals zero only if both terms are zero.

3. Set Each Term to Zero:
Therefore, for the equation [tex]\(x^2 + y^2 = 0\)[/tex] to hold true, both:
[tex]\[ x^2 = 0 \][/tex]
and
[tex]\[ y^2 = 0 \][/tex]

4. Solve for [tex]\(x\)[/tex] and [tex]\(y\)[/tex]:
If [tex]\(x^2 = 0\)[/tex], then the only solution is:
[tex]\[ x = 0 \][/tex]
Similarly, if [tex]\(y^2 = 0\)[/tex], then the only solution is:
[tex]\[ y = 0 \][/tex]

Therefore, the solution to the equation [tex]\(3x^2 + 3y^2 = 0\)[/tex] is:
[tex]\[ (x, y) = (0, 0) \][/tex]

This means both [tex]\(x\)[/tex] and [tex]\(y\)[/tex] must be zero to satisfy the original equation.

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