How many solutions the equations $2x−4y=29$ and $3x+1=0$ have?

Given: Equations $2x−4y=29$ and $3x+1=0$ 

To do: To find the number of solutions of the given pair of equtions.

The general form for a pair of linear equations in two variables $x$ and $y$ is $a_1x+b_1y+c_1=0$ and $a_2x+b_2y+c_2=0$

$2x−4y=29---( 1)$

$3x+1=0---( 2)$

Comparing equations $( 1)$ and $( 2)$ with the general form of equation to consider their co-efficient,

$a1=2,\ a2=3,\ b_1=−4,\ b_2=0$ So,  

Here $\frac{a_1}{a_2}=\frac{2}{3}$ and $\frac{b_1}{b_2}=\frac{-4}{0}$

$\Rightarrow \frac{a_1}{a_2}\
eq \frac{b_1}{b_2}$

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Which is said to be consistent.

Hence, the equations are consistent.