Question

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

Answer 1

y=-x+5/2..................(2)
the slopes of equations (10) & (2) are same and the intercepts are different
so the lines are parallel.
it has no solution

Answer 2

no solution.

Explanation:

The given system of equations is

`x+y=3`

`2x+2y=5`

If two equations are defined as
`ax_1+by_1+c_1=0\text{ and }ax_2+by_2+c_2=0`, and
`(a_1)/(a_2)=(b_1)/(b_2)\\eq (c_1)/(c_2)`, then lines are parallel.

In the given equations
`a_1=1,b_1=1,c_1=-3,a_2=2,b_2=2,c_2=-5`.

`(a_1)/(a_2)=(1)/(1)=1`

`(b_1)/(b_2)=(2)/(2)=1`

`(c_1)/(c_2)=(-3)/(-5)=(3)/(5)`

`(a_1)/(a_2)=(b_1)/(b_2)\\eq (c_1)/(c_2)`

So, the lines are parallel and parallel lines neven intersect each other.

Therefore, the given system of equation have no solution.