Turn which way?

Algebra Level 2

$\begin{aligned} \LARGE \color{#624F41}x + \frac {\color{#3D99F6} 4} {\color{#69047E}y} &=& \LARGE {\color{#3D99F6} 4} \\ \LARGE \color{#69047E}y + \frac {\color{#20A900} 6}{ \color{#624F41} x } &=& \LARGE {\color{#20A900} 6} \\ \LARGE \color{#624F41}x + \color{#69047E}y \ &=& \LARGE \ \color{grey} ? \end{aligned}$

11 \text{ or } \frac {12}{13}

7 \text{ or } \frac {17}{6}

6 \text{ or } \frac {16}{7}

10 \text{ or } \frac {20}{9}

5 \text{ or } \frac {15}{4}

9 \text{ or } \frac {29}{3}

0 \text{ or } \frac {10}{9}

15 \text{ or } \frac {25}{17}

4 solutions

Muhammad Fairuzi Teguh
May 1, 2015

$y+\frac { 6 }{ x } =6\quad \Rightarrow \quad y=6-\frac { 6 }{ x } \\$

subtitute to $x+\frac { 4 }{ y } =4$ we get $x+\frac { 4 }{ 6-\frac { 6 }{ x } } =4\\ \left( x+\frac { 4 }{ 6-\frac { 6 }{ x } } \right) \times \left( 6-\frac { 6 }{ x } \right) =4\left( 6-\frac { 6 }{ x } \right) \\ 6x-2=24-\frac { 24 }{ x } \\ x\left( 6x-2 \right) =x\left( 24-\frac { 24 }{ x } \right) \\ 6{ x }^{ 2 }-26x+24=0\\ (6x-8)(x-3)=0$

if $x=\frac { 4 }{ 3 } \quad \Rightarrow \quad y=\frac { 3 }{ 2 } \quad \Rightarrow \quad x+y=\frac { 17 }{ 6 }$

if $x=3\quad \Rightarrow \quad y=4\quad \Rightarrow \quad x+y=7$

The answer is $7$ or $\frac { 17 }{ 6 }$

Vinícius Ferreira
May 1, 2015

Muito bom! Very good. Nicely done.

Fabio Bittar - 6 years, 1 month ago

Malhar Deshpande
May 2, 2015

Can it be done with cramer's rule???

Siddharth Singh
Apr 26, 2015

xy+4=4y and xy+6=6y.From here we find y=3x-1/2.Then we substitute this value in 2nd equation,then the we find x=3 or 4/3. A gain substituting the value of x in the equation ,we find y=4 or 3/2. x+y = 7, 17/6

Turn which way?

4 solutions

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