Question

How many solutions does the system x + y = 3 and 2x + 2y = 5 have?

no solutions
one solution
two solutions
an infinite number of solutions

Answer 1

The answer to the question is no solutions

Answer 2

No solution

Explanation:

`x + y = 3` and
`2x + 2y = 5`

To find the number of solutions, lets solve each equation for y

`x + y = 3` , subtract x on both sides of the equation

`y = -x+3`

`2x + 2y = 5`, subtract x on both sides of the equation

`2y = -2x+5`, divide the whole equation by 2

`y = -x+(5)/(2)`

Now we look at the slope of both equations

The coefficient of x is the slope. slope of first and second equation is -1

Slopes are same , so they are parallel to each other

When the lines are parallel then there is no solution