contestada

use technology to determine an approximate solution to each of the following systems of linear equations
a y=22x-9.5 and y=2.5x+4.1
b 8x+y-18=0 and 5x+9y+4=0
c 6x + y= 12 and 5x +8y =-100

Respuesta :

From the given system of linear equations, we have;

  • a. x ≈ 0.697, y ≈ 5.84
  • b. x ≈ 2.48, y ≈ -1.82
  • c. x ≈ 4.56, y ≈ -15.35

How can technology be used to solve the given equations?

a. The system of linear equations can be expressed as follows;

y = 22•x - 9.5

y = 2.5•x + 4.1

Rewriting the equations to have the constants on the right, we have;

y - 22•x = - 9.5

y - 2.5•x = 4.1

Solving the above equations using matrices method on a calculator gives;

  • y = 5.84
  • x = 0.697

By direct solving, we have;

22•x - 9.5 = 2.5•x + 4.1

22•x - 2.5•x = 4.1 + 9.5

19.5•x = 13.6

x = 13.6 ÷ 19.5 ≈ 0.697

  • x ≈ 0.697

y = 22•x - 9.5

y = 22×(13.6/19.5) - 9.5 ≈ 5.84

  • y ≈ 5.84

b. 8•x + y - 18 = 0

5•x + 9•y + 4 = 0

Rewriting gives;

8•x + y = 18

5•x + 9•y = -4

Solving with technology gives,;

  • x ≈ 2.48
  • y ≈ -1.82

Solving directly gives;

  • y = 18 - 8•x
  • y = -(5•x + 4)/9

Which gives;

18 - 8•x = -(5•x + 4)/9

9×(18 - 8•x) = -(5•x + 4)

162 - 72•x = -(5•x + 4)

5•x - 72•x = -162 - 4 = -166

67•x = 166

x = 166 ÷ 67 ≈ 2.478

  • x ≈ 2.478

y = 18 - 8•x

Therefore;

y = 18 - 8 × (166 ÷ 67) ≈ -1.82

  1. y ≈ -1.82

c. 6•x + y = 12

5•x + 8•y = -100

Solving the above linear system using technology, we have;

  • x ≈ 4.56
  • y ≈ -15.35

Solving directly, we have;

y = 12 - 6•x

5•x + 8•y = -100

y = (-100 - 5•x)/8

12 - 6•x = (-100 - 5•x)/8

8 × (12 - 6•x) = (-100 - 5•x)

96 - 48•x = (-100 - 5•x)

48•x - 5•x = 96 + 100

43•x = 196

x = 196/43 ≈ 4.56

  • x ≈ 4.56

y = 12 - 6•x

Therefore;

y = 12 - 6×(196/43) ≈ -15.35

  • y ≈ -15.35

Learn more about linear equations here:

https://brainly.com/question/2226590

#SPJ1