Question

Determine the number of solutions for the systems
x+y=2 and 2x+2y=8

Answer 1

The number of solutions of the system is zero

Explanation:

we have

a)
`x+y=2`

Isolate the variable y

`y=-x+2` ----> equation A

This is the equation of the line in slope intercept form

where

The slope is m=-1

The y-intercept is b=2

b)
`2x+2y=8`

Isolate the variable y

`2y=-2x+8`

`y=-x+4` ----> equation B

This is the equation of the line in slope intercept form

where

The slope is m=-1

The y-intercept is b=4

Remember that

If two lines are parallel, then their slopes are the same

In this problem the lines A and B are parallel lines with different y-intercept

so

The lines don't intersect

therefore

The system has no solution