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

Question

asked Feb 7, 2019 62.9k views

2 Answers

Hkm Sadek · Answer 1 · 2019-02-12T18:26:30+0000

Answer:

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