Mathematics: Solve for x and y in the following set of equation 6x+5xy-5y=8 x+y=3 this is important

Solve for x and y in the following set of equation

Ответ:

sruthivada

31.12.2021

STEP 1:

$6x+5xy-5y=8\\ \\ 6x+5y\left( x-1 \right) =8\\ \\ 5y\left( x-1 \right) =8-6x\\ \\ 5y\left( x-1 \right) =2\left( 4-3x \right) \\ \\ \frac { 1 }{ 5\left( x-1 \right) } \cdot 5y\left( x-1 \right) =2\left( 4-3x \right) \cdot \frac { 1 }{ 5\left( x-1 \right) } \\ \\ y=\frac { 2\left( 4-3x \right) }{ 5\left( x-1 \right) }$

STEP 2:

$x+y=3\\ \\ y=3-x$

STEP 3:

This means that...

$3-x=\frac { 2\left( 4-3x \right) }{ 5\left( x-1 \right) } \\ \\ \left\{ 5\left( x-1 \right) \right\} \left( 3-x \right) =2\left( 4-3x \right) \\ \\ \left( 5x-5 \right) \left( 3-x \right) =8-6x\\ \\ 15x-5{ x }^{ 2 }-15+5x=8-6x\\ \\ 20x-5{ x }^{ 2 }-15=8-6x\\ \\ 5{ x }^{ 2 }+8-6x+15-20x=0\\ \\ 5{ x }^{ 2 }-26x+23=0$

STEP 4:

Which means that...

$\\ \frac { 1 }{ 5 } \cdot \left( 5{ x }^{ 2 }-26x+23 \right) =0\cdot \frac { 1 }{ 5 } \\ \\ { x }^{ 2 }-\frac { 26 }{ 5 } x+\frac { 23 }{ 5 } =0\\ \\ { x }^{ 2 }-\frac { 26 }{ 5 } x=-\frac { 23 }{ 5 }$

Which means that...

$\ \\ { \left( x-\frac { 13 }{ 5 } \right) }^{ 2 }-{ \left( \frac { 13 }{ 5 } \right) }^{ 2 }=-\frac { 23 }{ 5 } \\ \\ { \left( x-\frac { 13 }{ 5 } \right) }^{ 2 }-\frac { 169 }{ 25 } =-\frac { 23 }{ 5 } \\ \\ { \left( x-\frac { 13 }{ 5 } \right) }^{ 2 }=-\frac { 115 }{ 25 } +\frac { 169 }{ 25 } \\ \\ { \left( x-\frac { 13 }{ 5 } \right) }^{ 2 }=\frac { 54 }{ 25 }$

Which means that...

$\\ \\ x-\frac { 13 }{ 5 } =\pm \frac { \sqrt { 54 } }{ 5 } =\pm \frac { 3\sqrt { 6 } }{ 5 } \\ \\ \therefore \quad x=\frac { 13 }{ 5 } \pm \frac { 3\sqrt { 6 } }{ 5 }$

STEP 5:

When:

$x=\frac { 13 }{ 5 } +\frac { 3\sqrt { 6 } }{ 5 }$

.........

$y=3-\left( \frac { 13 }{ 5 } +\frac { 3\sqrt { 6 } }{ 5 } \right) \\ \\ y=\frac { 15 }{ 5 } -\frac { 13 }{ 5 } -\frac { 3\sqrt { 6 } }{ 5 } \\ \\ y=\frac { 15-13-3\sqrt { 6 } }{ 5 } \\ \\ y=\frac { 2-3\sqrt { 6 } }{ 5 }$

STEP 6:

When :

$x=\frac { 13 }{ 5 } -\frac { 3\sqrt { 6 } }{ 5 }$

...........

$y=3-\left( \frac { 13 }{ 5 } -\frac { 3\sqrt { 6 } }{ 5 } \right) \\ \\ y=\frac { 15 }{ 5 } -\frac { 13 }{ 5 } +\frac { 3\sqrt { 6 } }{ 5 } \\ \\ y=\frac { 15-13+3\sqrt { 6 } }{ 5 } \\ \\ y=\frac { 2+3\sqrt { 6 } }{ 5 }$

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Ответ:

mqturner1989Kedie

25.03.2021

Mathematics

FV= $11,156.94

Step-by-step explanation:

Giving the following information:

Initial investment (PV)= $7,000

Number of periods (n)= 8 years

Interest rate (i)= 6% compounded annually

To calculate the future value (FV), we need to use the following formula:

FV= PV*(1 + i)^n

FV= 7,000*(1.06^8)

FV= $11,156.94

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Solve for x and y in the following set of equation
6x+5xy-5y=8
x+y=3
this is important

Ответ:

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