Mathematics
msbeauty
16

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

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(1) Answers
Travelstead238

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

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