How many solutions does the following system of equations have? y=5/2x+2 and 2y=5x+8
Mathematics · Middle School · Tue Nov 03 2020
Answered on
We have,
y=5/2x+2 and 2y=5x+8
Now, y = 5/2x + 2
y = (5x + 4)/2
2y = 5x + 4
5x - 2y + 4 = 0 ….1
And ,2y = 5x + 8
So, 5x - 2y + 8 = 0 …2
a1 = 5 , b1 = -2 , c1 = 4
a2 = 5, b2 = -2 , c2 = 8
So, a1/a2 = 5/5 = 1
b1/b2 = -2/-2 = 1
And, c1/c2 = 4/8 = 1/ 2
So, a1/a2 = b1/b2 ≠ c1/c2
That means given equations have no solutions
Answered on
For finding how many solution can have a system of equations we do
a(2)/a(3)=b(1)/b(2)=c(1)/c(2)….(1)
Form the Given equations
y=5/2x+2 where a(1)= 5/2,b(1)= 2
and 2y=5x+8 , simplify y=5x/2+4 ,where a(2)= 5/2,b(2)= 4
By equation (1)
(5/2)/(5/2)=2/4
1=½
So for the given equations a(2)/a(3)=b(1)/b(2)=c(1)/c(2) not equal This means that there are no values of x such that these two lines are equal, hence they are parallel and there are no solutions.