Solve this system of equations by substitution: −3x + 3y = 3 and −5x + y = 13
2 answers:
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Multiply the equation:
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
Multiplying this by 3 (or whatever number, for all it matters) gives
Now, a product is zero if and only if at least one of the factor is zero. So, either or
Since the first is clearly impossible, the second one must be true, which is the original equation.