Question

How do you find the system of equations $y=9$ and $7x-6y=-12$

Answer 1

Hint: Now we are given with two linear equations. To find the solution of the equation we will use a method of substitution. Now from the first equation we know that the value of y is 9. Hence on substituting y = 9 in the second equation we will get the value of x. Hence we have the solution of the given equation.

Complete step by step solution:
Now we are given with two linear equations.
Now we want to find the solution to these two equations. Which means we want to find the values of x and such that it satisfies both the equations.
We will find the solution to the equation by method of substitution.
Now we know that according to the first equation we have y = 9.
Hence substituting y = 9 in the equation $7x-6y=-12$ we get,
$\Rightarrow 7x-6\left( 9 \right)=-12$
Now on simplifying the equation we get,
$\begin{align}
  & \Rightarrow 7x-54=-12 \\
 & \Rightarrow 7x=54-12 \\
 & \Rightarrow 7x=42 \\
\end{align}$
Now dividing the whole equation by 7 we get, x = 6.

Hence the solution of the two simultaneous equation is x = 6 and y = 9.

Note: Now note that here we have equation as y = 9. This is an equation in the XY plane but we do not have x variable here. This is because the equation is independent of x. The meaning of the equation is nothing but whatever be the value of x the value of y is 9. Now to understand this geometrically the equation represents a line passing through (0, 9) and parallel to the x axis.
Also note that this is still a linear equation in two variables of the form $0x+1y=9$ and hence represents a line and not a point.