Question

Determine Number of Solutions in System

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

Answer 1

• -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 .

Answer 2

no solutions

Explanation:

Given equations:

• Equation 1:
  `-x+y=8`
• Equation 2:
  `2x-2y=-14`

Rewrite the given equations to make y the subject:

Equation 1

`-x+y=8`

`\implies y=x+8`

Equation 2

`2x-2y=-14`

`\implies 2y=2x+14`

`\implies y=x+7`

Slope-intercept form of a linear equation:
`y=mx+b`

(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.