How many solutions does the system x + y = 3 and 2x + 2y = 5 have?
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:
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 \(\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}
eq \dfrac{c_1}{c_2}\), then lines are parallel.
In the given equations \(a_1=1,b_1=1,c_1=-3,a_2=2,b_2=2,c_2=-5\).
\(\dfrac{a_1}{a_2}=\dfrac{1}{1}=1\)
\(\dfrac{b_1}{b_2}=\dfrac{2}{2}=1\)
\(\dfrac{c_1}{c_2}=\dfrac{-3}{-5}=\dfrac{3}{5}\)
\(\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}
eq \dfrac{c_1}{c_2}\)
So, the lines are parallel and parallel lines neven intersect each other.
Therefore, the given system of equation have no solution.