Question

Write two solutions of the form $x = 0$, $y = a$ and \[x = b\], \[y = 0\] for each of the following equations:
(i) \[5x - 2y = 10\]
(ii) \[ - {\text{ }}4x + 3y = 12\]
(iii) \[2x + 3y = 24\]

Answer 1

Hint: For the solution of the form $x = 0$ and $y = a$, we will substitute the value 0 for $x$, to find the value of $y = a$. Similarly, to find the solution of the form \[x = b\] and \[y = 0\], substitute 0 for $y$ to find the value \[x = b\].

Complete step by step answer:

We have to find solution of the given equations of the form $x = 0$, $y = a$ and \[x = b\], \[y = 0\]
In (i) part, we have the equation of the line \[5x - 2y = 10\]
Substitute 0 for $x$ in the above equation, then we have
$
  5\left( 0 \right) - 2y = 10 \\
   \Rightarrow - 2y = 10 \\
   \Rightarrow y = - 5 \\
$
Similarly, now we will substitute 0 for $y$
$
  5x - 2\left( 0 \right) = 10 \\
   \Rightarrow 5x = 10 \\
   \Rightarrow x = 2 \\
$
Hence, solutions are \[x = 0,{\text{ }}y = - 5\] and \[x = 2,y = 0\].
Next, in part (ii) we have the equation of line as \[ - {\text{ }}4x + 3y = 12\]
Substitute 0 for $x$ in the above equation, then we have
$
   - 4\left( 0 \right) + 3y = 12 \\
   \Rightarrow 3y = 12 \\
$
Divide the equation throughout by 3,
\[y = 4\]
Similarly, now we will substitute 0 for $y$
$
   - 4x + 3\left( 0 \right) = 12 \\
   \Rightarrow - 4x = 12 \\
$
Divide the equation throughout by $ - 4$,
\[x = - 3\]
Hence, solutions are \[x = 0,{\text{ }}y = 4\] and \[x = - 3,y = 0\].
Next, in part (iii) we have the equation of line as \[2x + 3y = 24\]
Substitute 0 for $x$ in the above equation, then we have
$
  2\left( 0 \right) + 3y = 24 \\
   \Rightarrow 3y = 24 \\
$
Divide the equation throughout by 3,
\[y = 8\]
Similarly, now we will substitute 0 for $y$
$
  2x + 3\left( 0 \right) = 24 \\
   \Rightarrow 2x = 24 \\
$
Divide the equation throughout by 2,
\[x = 12\]
Hence, solutions are \[x = 0,{\text{ }}y = 8\] and \[x = 12,y = 0\].

Note: The solution of the form \[x = 0\] and \[y = a\] is the point where the line intersects \[y\] axis and the point of the form $x = b$ and $y = 0$ is the point where the line intersects $x$ axis. Substitution of the values should be correct in order to get right answer.