Question

Solve the system of equations.

Answer 1

Answer:

1) {y,x}={-3,-23}

2) {x,y}={7,-9/2}

Step-by-step explanation:

Required:

• Solve systems of equations

1) y - x = 20, 2x - 15y = -1

Equations Simplified or Rearranged :

[1]    y - x = 20

  [2]    -15y + 2x = -1

Graphic Representation of the Equations :

x + y = 20        2x - 15y = -1  

Solve by Substitution :

// Solve equation [1] for the variable  y

 [1]    y = x + 20

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

  [2]    -15•(x +20) + 2x = -1

  [2]     - 13x = 299

// Solve equation [2] for the variable  x

[2]    13x = - 299

  [2]    x = - 23

// By now we know this much :

  y = x+20

   x = -23

// Use the  x  value to solve for  y

   y = (-23)+20 = -3

Solution :

{y,x} = {-3,-23}

2) 25-x=-4y,3x-2y=30

Equations Simplified or Rearranged :

  [1]    -x + 4y = -25

  [2]    3x - 2y = 30

Graphic Representation of the Equations :

   4y - x = -25        -2y + 3x = 30  

Solve by Substitution :

// Solve equation [1] for the variable  x

  [1]    x = 4y + 25

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

 [2]    3•(4y+25) - 2y = 30

  [2]    10y = -45

// Solve equation [2] for the variable  y

  [2]    10y = - 45

  [2]    y = - 9/2

// By now we know this much :

  x = 4y+25

   y = -9/2

// Use the  y  value to solve for  x

  x = 4(-9/2)+25 = 7

Solution :

{x,y} = {7,-9/2}