Question

question 22 of 25
how many solutions does the following system of equations have?
\\( y = \frac{5}{2}x + 2 \\)
\\( 2y = 5x + 4 \\)
a. infinitely many
b. zero
c. one
d. two

Explanation:

Step1: Simplify the second equation

To see the relationship between the two equations, we simplify the second equation \(2y = 5x + 4\) by dividing both sides by 2.
\(y=\frac{5x + 4}{2}=\frac{5}{2}x+2\)

Step2: Compare the two equations

Now we have the first equation \(y=\frac{5}{2}x + 2\) and the simplified second equation \(y=\frac{5}{2}x+2\). Since both equations are identical (same slope and same y - intercept), they represent the same line.

Answer:

A. Infinitely many