Question

Solve for x and y. 4x-3y=16 -2x+4y=-2 DUE 2/7/17!

Answer 1

$\left \{ {{4x-3y=16\:(I)} \atop {-2x+4y=-2\:(II)}} \right.$

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)
$\frac{20x}{\diagup\!\!\!\!5} - \frac{36}{\diagup\!\!\!\!5} = \frac{80}{\diagup\!\!\!\!5}$
$20x - 36 = 80$
$20x = 80 + 36$
$20x = 116$
$x = \frac{116}{20} \frac{\div4}{\div4} \to\: \boxed{\boxed{x = \frac{29}{5} }}\end{array}}\qquad\quad\checkmark$