Question

I will give you 30points

y = x + 4
5x + 3y = -4
Help please system by substitution

And help with y = 2x and
-8x – 2y = 24

Answer 1

1)
`{y,x}={2,-2}`

2)
`{y,x} = {-4,-2}`

Explanation:

1)
`y=x+4 \\ 5x+3y=-4` <---------- given linear equations

Equations Simplified or Rearranged :

`y - x = 4 \\3y + 5x = -4`

Graphic Representation of the Equations : PICTURE #1

`x + y = 4 \\5x + 3y = -4`

Solve by Substitution :

// Solve equation [1] for the variable y

`[1] y = x + 4`

// Plug this in for variable y in equation [2]

`3*(x +4) + 5x = -4 \\ [2] 8x = -16`

// Solve equation [2] for the variable x

`8x = - 16 x = - 2`

// By now we know this much :

`y = x+4\\ x = -2`

// Use the x value to solve for y

`y = (-2)+4 = 2`

Solution :

`{y,x} = {2,-2}`

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2)
`y=2x \\-8x-2y=24` <----- linear equations given

Equations Simplified or Rearranged :

`y - 2x = 0 \\ -2y - 8x = 24`

Graphic Representation of the Equations : PICTURE #2

`-2x + y = 0 \\\\-8x - 2y = 24`

Solve by Substitution :

// Solve equation [1] for the variable y

`[1] y = 2x`

// Plug this in for variable y in equation [2]

`[2] -2*(2x) - 8x = 24\\ [2] - 12x = 24`

// Solve equation [2] for the variable x

`[2] 12x = - 24 [2] x = - 2`

// By now we know this much :

`y = 2x \\ x = -2`

// Use the x value to solve for y

`y = 2(-2) = -4`

Solution :

`{y,x} = {-4,-2}`

Answer 2

1)

y = x + 4

5x + 3y = -4

5x + 3(x + 4) = -4

5x + 3x + 12 = -4

8x + 12 = -4

8x = -4 -12

8x = -16

x = -2

substitute x into the equation

y = -2 + 4

y = 2

Answers : x = -2 , y = 2