For the following equations, what are the values of a and b to have infinitely many solutions?
ax + by = 2
3x - (5 - 2a)y = 6

Correct option is C

Solution:

ax + by = 2

3x - (5 - 2a)y = 6

To find the values of a and b that make the system of equations have infinitely many solutions, we use the condition that two equations must be proportional to each other.

The proportionality condition is:

​$$\frac{a}{3} = \frac{b}{-(5 - 2a)} = \frac{2}{6}$$​​

From the third part of the ratio, $$\frac{2}{6 }= \frac{1}{3}$$​, so we have:

$$\frac{a}{3}= \frac{1}{3}$$​ (equating the first part of the ratio),

This gives a = 1.

Substitute a = 1 into the second ratio:

​$$\frac{b}{-(5 - 2a) }= \frac{1}{3}$$​​

Substituting a = 1:

​$$\frac{b}{-3} = \frac{1}{3}$$​​

Solving for b gives: b = -1

Therefore, the values of a and b that make the system have infinitely many solutions are a = 1 and b = -1.