Question

Determine the number of solutions to each system of equations.

Please put all of the equations in either One Solution, No Solution, or Infinitely Many Solution boxes
DUE TONIGHT

Answer 1

the first answer is correct

Explanation:

Answer 2

One Solution:

• y=0.5x-2 ; y=-0.5x+4
• y=2x+1 ; y=-4x+1

No Solution:

• y=0.5x+1 ; y=0.5x+5
• y=-x-3 ; y=-x+3

Infinity many solutions:

• y=-x-2 ; y=-x-2
• y=3x+2.5 ; y=3x+2.5

Explanation:

We will see the system of equations one by one.

First system of Equation:

`y = 0.5x-2\\y=-0.5x+4`

It can clearly be seen that the two lines formed by the given equations are in opposite direction and they will have one intersection point so only one solution

Second System of Equation:

`y=0.5x+5\\y=0.5x+1`

This system also has no solution as the equations represent parallel lines and if we try to solve them we will get the solution in the form 0 = constant.

Third System of Equations:

`y =2x+1\\y = -4x+1`

The given equations will have a unique solution because the lines have different slopes or when graphed, they will have an intersection point.

Fourth System of Equations:

`y=3x+2.5\\y=3x+2.5`

The lines formed by these lines will overlap each other so there will be infinity many solutions.

Fifth System of Equations:

`y=-x-3\\y=-x+3`

These equations represent parallel lines so there will be no solution.

Sixth System of Solution:

`y=-x-2\\y=-x-2\\`

The system will have infinite number of solutions

Hence,

One Solution:

• y=0.5x-2 ; y=-0.5x+4
• y=2x+1 ; y=-4x+1

No Solution:

• y=0.5x+1 ; y=0.5x+5
• y=-x-3 ; y=-x+3

Infinity many solutions:

• y=-x-2 ; y=-x-2
• y=3x+2.5 ; y=3x+2.5