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The solution is checked in the other original equation to confirm that the ordered pair satisfies the entire system, not just the single equation used for back-substitution. If the pair was found by substituting into the first equation, checking it in the second equation verifies that both equations are simultaneously true for those values.

Conditions: A candidate ordered pair has been found.; At least one original equation remains available for substitution checking.; The equation used for back-substitution is not reused for the check.

The solution is checked in the other original equation to confirm that the ordered pair satisfies the entire system, not just the single equation used for back-substitution. If the pair was found by substituting into the first equation, checking it in the second equation verifies that both equations are simultaneously true for those values.

Conditions: A candidate ordered pair has been found.; At least one original equation remains available for substitution checking.; The equation used for back-substitution is not reused for the check.

The fraction $\frac{22}{20}$ simplifies to $\frac{11}{10}$ by dividing both the numerator and the denominator by their greatest common factor, which is 2. Since $22 \div 2 = 11$ and $20 \div 2 = 10$, the reduced fraction is $\frac{11}{10}$.

Conditions: The numerator (22) and denominator (20) share a common factor greater than 1.; The same nonzero factor (2) divides both the numerator and the denominator.

The fraction $\frac{22}{20}$ simplifies to $\frac{11}{10}$ by dividing both the numerator and the denominator by their greatest common factor, which is 2. Since $22 \div 2 = 11$ and $20 \div 2 = 10$, the reduced fraction is $\frac{11}{10}$.

Conditions: The numerator (22) and denominator (20) share a common factor greater than 1.; The same nonzero factor (2) divides both the numerator and the denominator.

The equation is multiplied by 3 to clear the denominators and eliminate the fractions. Since the denominators present are 1 and 3, the common denominator is 3.

Conditions: The equation contains fractional terms with denominators 1 and 3.; All terms on both sides of the equation are multiplied by the same nonzero number (3).

The equation is multiplied by 3 to clear the denominators and eliminate the fractions. Since the denominators present are 1 and 3, the common denominator is 3.

Conditions: The equation contains fractional terms with denominators 1 and 3.; All terms on both sides of the equation are multiplied by the same nonzero number (3).