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Solve the system of equations.

Solve the system of equations.-example-1
Solve the system of equations.-example-1
Solve the system of equations.-example-2
User Mvanallen
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1 Answer

12 votes
12 votes

Answer:

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

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

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}

Solve the system of equations.-example-1
Solve the system of equations.-example-2
User Boris K
by
3.5k points