Question

Solve each system of equations by showing the process of substitution.

Answer 1

Answer:

Step-by-step explanation:

a) y = -1/4x    --------------(I)

x + 2y = 4 -----------------(II)

Substitute y = (-1/4)x in equation (I)

$x + 2*\dfrac{-1}{4}x=4\\\\\\x -\dfrac{1}{2}x=4\\\\Multiply \ the \ entire \ equation \ by \ 2 \\\\2x -x = 8\\\\x=8$

$Substitute \ x = 8 \ in \ equation \ (I)\\\\y=\dfrac{-1}{4}*8\\\\\\y = -2$

Answer: x = 8  ; y = -2

b) y = -x - 2 --------------(i)

   3x + 3y = 6   -----------(ii)

Divide equation (ii) by m

x + y = 2

  y = -x + 2  ----(iii)

From (i) and (iii), it shows that these lines have same slope. So, they are parallel lines

Answer: No solution

3) -8x + 2y =4

            2y = 8x + 4

Divide the entire equation by 2

             y = 4x + 2 -------------(i)

            y = 4x + 2 ----------------(ii)

From (i) and (ii), we come to know that these lines coincide.So, they have infinite solutions.

Answer 2

Answer:

A. {x,y}={-2,-3}

// Solve equation [2] for the variable  x

 [2]    x = 2y + 4

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

  [1]    (2y+4) - y = 1

  [1]    y = -3

// Solve equation [1] for the variable  y

  [1]    y = - 3

// By now we know this much :

   x = 2y+4

   y = -3

// Use the  y  value to solve for  x

x = 2(-3)+4 = -2

B.   [1]           3x=3y-6

 [2]           y=x+2

Equations Simplified or Rearranged :

  [1]    3x - 3y = -6

  [2]    -x + y = 2

Solve by Substitution :

// Solve equation [2] for the variable  y

 [2]    y = x + 2

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

  [1]    3x - 3•(x +2) = -6

  [1]    0 = 0 =>  Infinitely many solutions

C.Step by Step Solution

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System of Linear Equations entered :

  [1]    4x - y = 2

  [2]    8x - 2y = 4

Solve by Substitution :

// Solve equation [1] for the variable  y

 [1]    y = 4x - 2

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

  [2]    8x - 2•(4x-2) = 4

  [2]    0 = 0 =>  Infinitely many solutions