Statement 1: If system of equations `2x+3y=a` and `bx +4y=5` has infinite solutions, then `a=(15)/(4),b=(8)/(5)`
Statement 2: Straight lines `a_(1)x+b_(1)y+c_(1)=0` and `a_(2)x+b_(2)y+c_(2)=0` are parallel if `a_(1)/(a_(2))=b_(1)/(b_(2))nec_(1)/c_(2)`

Answer

To solve the problem, we need to analyze both statements one by one.

### Statement 1:
We have a system of equations:
1. \( 2x + 3y = a \) (Equation 1)
2. \( bx + 4y = 5 \) (Equation 2)

For the system to have infinite solutions, the two lines represented by these equations must be coincident. This means that the ratios of the coefficients of \(x\), \(y\), and the constant terms must be equal.

Thus, we can set up the following ratios:
\[ \frac{2}{b} = \frac{3}{4} = \frac{a}{5} \]

#### Step 1: Find \(b\)
From the first two ratios:
\[ \frac{2}{b} = \frac{3}{4} \]
Cross-multiplying gives:
\[ 2 \cdot 4 = 3 \cdot b \implies 8 = 3b \implies b = \frac{8}{3} \]

#### Step 2: Find \(a\)
Now we use the third ratio:
\[ \frac{3}{4} = \frac{a}{5} \]
Cross-multiplying gives:
\[ 3 \cdot 5 = 4 \cdot a \implies 15 = 4a \implies a = \frac{15}{4} \]

Thus, we have found:
- \( a = \frac{15}{4} \)
- \( b = \frac{8}{3} \)

However, the statement claims \( b = \frac{8}{5} \), which is incorrect. Therefore, Statement 1 is **false**.

### Statement 2:
The second statement claims that two lines given by:
1. \( a_1x + b_1y + c_1 = 0 \)
2. \( a_2x + b_2y + c_2 = 0 \)

are parallel if:
\[ \frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2} \]

#### Step 3: Analyze the condition for parallel lines
For two lines to be parallel, their slopes must be equal. The slope of the first line is:
\[ -\frac{a_1}{b_1} \]
The slope of the second line is:
\[ -\frac{a_2}{b_2} \]
Setting these slopes equal gives:
\[ -\frac{a_1}{b_1} = -\frac{a_2}{b_2} \implies \frac{a_1}{b_1} = \frac{a_2}{b_2} \]

The condition that the lines are not coincident (and hence parallel) requires that the ratio of the constant terms is not equal:
\[ \frac{c_1}{c_2} \neq \frac{a_1}{a_2} \]

Thus, Statement 2 is **true**.

### Final Conclusion:
- Statement 1 is **false**.
- Statement 2 is **true**.