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

Answer:

no solution.

Step-by-step 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 $\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq \dfrac{c_1}{c_2}$, then lines are parallel.

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

$\dfrac{a_1}{a_2}=\dfrac{1}{1}=1$

$\dfrac{b_1}{b_2}=\dfrac{2}{2}=1$

$\dfrac{c_1}{c_2}=\dfrac{-3}{-5}=\dfrac{3}{5}$

$\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq \dfrac{c_1}{c_2}$

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

Therefore, the given system of equation have no solution.