5𝑥−𝑦=2𝑦+45x−y=2y+4𝑏𝑦=3+5𝑥by=3+5xIn the given system of equations, 𝑏b is a constant. If the system has no solution, what is the value of 𝑏b?

To find the value of b when the system has no solution, we need to make the two equations parallel. This happens when their slopes are equal.

The slope-intercept form of a linear equation is y = mx + c, where m is the slope.

Let's convert the given equations into slope-intercept form:

1. 5x - y = 2y + 4 Subtract 2y from both sides: 5x - 3y = 4 Divide by -3: y = 5/3x - 4/3 So, the slope of the first equation is 5/3.

2. by = 3 + 5x Subtract 3 from both sides: by - 3 = 5x Divide by b: y = 5/bx - 3/b So, the slope of the second equation is 5/b.

For the two lines to be parallel, their slopes must be equal. So, we set 5/3 equal to 5/b and solve for b:

5/3 = 5/b Cross-multiply: 5b = 15 Divide by 5: b = 15/5 = 3

So, the value of b for which the system has no solution is 3.