Question

I will give you 30points

Answer 1

Answer:

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

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

Step-by-step 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