Question

Write each of the following in the form of $ax+by+c=0$ and find the value of a, b and c.
a) $x=-5$
b) $y=2$
c) $2x=3$
d) $5y=-3$

Answer 1

Hint: Here, convert all the equations given in the form of $ax+by+c=0$ by taking every term to the left side. And whichever variable is absent, consider its coefficient as zero and proceed. Then compare the equation so obtained with $ax+by+c=0$ and find the values of a, b and c.

Complete step-by-step answer:

Here, we have to write all the equations given in the form $ax+by+c=0$ and then we have to find the value of a, b and c.

We know that the equation in two variables is of the form $ax+by+c=0$, where a is the x coefficient, b is the y coefficient and c is a constant.

(i) $x=-5$

Here, take -5 to the left side, -5 becomes 5 then,

$\Rightarrow x+5=0$

This equation can be written as:

$\begin{align}

  & x+0+5=0 \\

 & \Rightarrow 1x+0y+5=0 \\

\end{align}$

Now, comparing the above equation with the general form $ax+by+c=0$, we will get:

a = 1, b = 0 and c=5

(ii) $y=2$

Here also take 2 to the left side, 2 becomes -2,

$\begin{align}

  & \Rightarrow y-2=0 \\

 & \Rightarrow 0+y-2=0 \\

 & \Rightarrow 0+y-2=0 \\

 & \Rightarrow 0+y-2=0 \\

 & \Rightarrow 0x+1y+(-2)=0 \\

\end{align}$

Now, comparing this equation with the general equation, we get:

a = 0, b = 1 and c = -2

(iii) $2x=3$

Now, take 3 to the left side, 3 becomes -3. Then, the equation,

$\begin{align}

  & \Rightarrow 2x-3=0 \\

 & \Rightarrow 2x+0-3=0 \\

 & \Rightarrow 2x+0y+(-3)=0 \\

\end{align}$

Next, by comparing the above equation with the general equation, we obtain:

a = 2, b = 0 and c = -3

(iv) $5y=-3$

Now, by taking -3 to the lefts side, -3 becomes 3 and we get the equation,

$\begin{align}

  & \Rightarrow 5y+3=0 \\

 & \Rightarrow 0+5y+3=0 \\

 & \Rightarrow 0x+5y+3=0 \\

\end{align}$

Again, comparing the above equation with the general equation $ax+by+c=0$, we get:

a = 0, b = 5 and c = 3

Note: Here, the linear equation of two variables is written in the form $ax+by+c=0$ where, a, b and c are real numbers. The solution of such an equation is a pair of values, one for x and the other for y which further makes the two sides of an equation equal. Basically a linear equation in two variables will have an infinite number of solutions.