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Determine Number of Solutions in System

Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.

Determine Number of Solutions in System Determine if the following system of equations has no solutions infinitely many solutions or exactly one solution class=

Respuesta :

  • -x+y=8=>y=8+x
  • 2x-2y=-14=>x-y=-7=>-x+y=7=>y=7+x

As both left side is same

  • Slopes are equal

There is no solutions .

semsee45

Answer:

no solutions

Step-by-step explanation:

Given equations:

  • Equation 1:  [tex]-x+y=8[/tex]
  • Equation 2:  [tex]2x-2y=-14[/tex]

Rewrite the given equations to make y the subject:

Equation 1

[tex]-x+y=8[/tex]

[tex]\implies y=x+8[/tex]

Equation 2

[tex]2x-2y=-14[/tex]

[tex]\implies 2y=2x+14[/tex]

[tex]\implies y=x+7[/tex]

Slope-intercept form of a linear equation:  [tex]y=mx+b[/tex]

(where m is the slope and b is the y-intercept)

As both equations have the same slope, the lines are parallel and therefore there is no solution to the system of equations as the lines do not intersect.

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