Question

How do you solve the system of equation $x+5y=-7$ and $6x-8y=-24$

Answer 1

Hint: Now we are given a pair of linear equations in two variables. Now to solve the equation we will first consider the equation $x+5y=-7$ . With the help of this equation we represent x in terms of y. Hence now we have a value of x. Now we will substitute this value of x in the other equation. Hence we will get a linear equation in y. We will simplify the equation obtained and solve it to find the value of y. Now once we have y we will substitute its value in any equation and find x.

Complete step by step solution:
Now we are given with a pair of linear equations in two variables x and y.
Now to solve the linear equation we will use a method of substitution.
To do so let us first consider the linear equation $x+5y=-7$
Now on rearranging the terms in the equation we get, $x=-7-5y$
Now we have represented x in terms of y. Hence we will substitute the obtained value of x in another equation so we get a linear equation in one variable.
Hence we get,
$\begin{align}
  & \Rightarrow 6\left( -7-5y \right)-8y=-24 \\
 & \Rightarrow -42-30y-8y=-24 \\
 & \Rightarrow -42-38y=-24 \\
 & \Rightarrow -38y=42-24 \\
 & \Rightarrow -38y=18 \\
 & \Rightarrow y=-\dfrac{18}{38} \\
\end{align}$
Hence we have the value of y. Now substituting this value in $x=-7-5y$ we get,
$\begin{align}
  & \Rightarrow x=-7-5\left( -\dfrac{18}{38} \right) \\
 & \Rightarrow x=-7+\dfrac{90}{38} \\
 & \Rightarrow x=\dfrac{90-266}{38} \\
 & \Rightarrow x=\dfrac{-88}{19} \\
\end{align}$

Hence we get the solution of the equation as $x=\dfrac{-88}{19}$ and $y=\dfrac{-18}{38}$

Note: Now note that we can also solve the equation by plotting graphs of the two equations. We will consider the equation and find points (x, y) which satisfy the equation. Now draw a line passing through all the points. Hence we get a graph of the equation. Now the solution of two linear equations is nothing but the intersection points of the graph of the equation.