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Liono4ka [1.6K]
3 years ago
8

Multiply the equation 2x+2y=8 by 3. Does the equation have the same solution set?

Mathematics
1 answer:
stepan [7]3 years ago
3 0

Multiply the equation:

2x+2y=8 \mapsto 6x+6y=24

The solution set is the same, because multiplying both sides of an equation by a non-zero number doesn't change the solution set. In fact, if you rewrite the equation as

2x+2y-8=0

Multiplying this by 3 (or whatever number, for all it matters) gives

3(2x+2y-8)=0

Now, a product is zero if and only if at least one of the factor is zero. So, either 3=0 or 2x+2y-8=0

Since the first is clearly impossible, the second one must be true, which is the original equation.

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