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The two equations can be added directly to eliminate $y$ because their $y$-coefficients are exact opposites ($-4y$ and $+4y$). When equations with opposite coefficients for the same variable are added term by term, those terms cancel out to zero, leaving a one-variable equation in $x$.

Conditions: The system has been reduced to integer coefficients: $3x - 4y = 14$ and $15x + 4y = 22$.; The equations are aligned term-by-term before addition.

The two equations can be added directly to eliminate $y$ because their $y$-coefficients are exact opposites ($-4y$ and $+4y$). When equations with opposite coefficients for the same variable are added term by term, those terms cancel out to zero, leaving a one-variable equation in $x$.

Conditions: The system has been reduced to integer coefficients: $3x - 4y = 14$ and $15x + 4y = 22$.; The equations are aligned term-by-term before addition.

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).