\(\left \{ {{4x-3y=16\:(I)} \atop {-2x+4y=-2\:(II)}} \right.\)
Multiply the 2nd equation by (-4). This will eliminate the x's when you add the two new equations together.
\(\left \{ {{4x-3y=16\:\:\:\:\:\:\:\:\:\:} \atop {-2x+4y=-2\:*(-4)}} \right.\)
\(\left \{ {{\diagup\!\!\!\!4x-3y=16} \atop {-\diagup\!\!\!\!4x+8y=-4}} \right.\)
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\(5y = 12\)
\(\boxed{\boxed{y = \frac{12}{5}}}\end{array}}\qquad\quad\checkmark\)
Let's replace the value found in the first equation:
\(4x-3y=16\:(I)\)
\(4x-3*( \frac{12}{5}) =16\)
\(4x - \frac{36}{5} = 16\)
least common multiple (5)
\(\frac{20x}{\diagup\!\!\!\!5} - \frac{36}{\diagup\!\!\!\!5} = \frac{80}{\diagup\!\!\!\!5}\)
\(20x - 36 = 80\)
\(20x = 80 + 36\)
\(20x = 116\)
\(x = \frac{116}{20} \frac{\div4}{\div4} \to\: \boxed{\boxed{x = \frac{29}{5} }}\end{array}}\qquad\quad\checkmark\)
