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3 years ago

Solve the system using substitution: y = -6x + 7 3x – 2y = 16 helppp

Mathematics

2 answers:

bearhunter [10]3 years ago

7 0

Answer:

x=-6 y=-1

Step-by-step explanation:

// Solve equation [2] for the variable y

[2] y = -x - 7

// Plug this in for variable y in equation [1]

[1] 3x - 2•(-x -7) = -16

[1] 5x = -30

// Solve equation [1] for the variable x

[1] 5x = - 30

[1] x = - 6

// By now we know this much :

x = -6

y = -x-7

// Use the x value to solve for y

y = -(-6)-7 = -1

Solution :

{x,y} = {-6,-1}

marissa [1.9K]3 years ago

6 0

Answer: 1 .x=-1/6y+7/6 (2.x=2/3y+16/3

Step-by-step explanation:

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marusya05 [52]

$\large\underline{\sf{Solution-}}$

We have to find out the value of the fraction.

Let us assume that:

$\sf \longmapsto x =2 + \dfrac{1}{2 + \dfrac{1}{2 + \dfrac{1}{2 + ... \infty} } }$

We can also write it as:

$\sf \longmapsto x =2 + \dfrac{1}{x}$

$\sf \longmapsto x =\dfrac{2x + 1}{x}$

$\sf \longmapsto {x}^{2} =2x + 1$

$\sf \longmapsto {x}^{2} - 2x - 1 = 0$

Comparing the given equation with ax² + bx + c = 0, we get:

$\sf \longmapsto\begin{cases} \sf a =1 \\ \sf b = - 2 \\ \sf c = - 1 \end{cases}$

By quadratic formula:

$\sf \longmapsto x = \dfrac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a}$

$\sf \longmapsto x = \dfrac{2 \pm \sqrt{ {( - 2)}^{2} - 4(1)( - 1)} }{2 \times 1}$

$\sf \longmapsto x = \dfrac{2 \pm \sqrt{4 + 4} }{2 \times 1}$

$\sf \longmapsto x = \dfrac{2 \pm \sqrt{8} }{2}$

$\sf \longmapsto x = \dfrac{2 \pm2 \sqrt{2} }{2}$

$\sf \longmapsto x = 1 \pm\sqrt{2}$

$\sf \longmapsto x = \begin{cases} \sf 1 + \sqrt{2} \\ \sf 1 - \sqrt{2} \end{cases}$

But "x" cannot be negative. Therefore:

$\sf :\implies x = 1 + \sqrt{2}$

So, the value of the fraction is 1 + √2.

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Ilia_Sergeevich [38]

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