Question

How do you solve \[2x-3y=-2\] and $4x+y=24$ ?

Answer 1

Hint: Now to solve the given equation we will consider the equation $4x+y=24$ and use the equation to write y in terms of x. now we will substitute the obtained value of y in the other equation. Hence we get a linear equation in x. Now we will solve the equation to find the value of x. Hence we will substitute the value of x in any equation and find the value of y.

Complete step by step solution:
Now we are given with two linear equations in x and y.
We will find the solution of the equation by using a method of substitution.
To do so we will first consider the equation $4x+y=24$ .
Now we will try to write y in terms of x.
To do so we will transpose 4x from LHS to RHS. Hence we get,
$y=24-4x$
Now we have written y in terms of x. Hence we will substitute the obtained value of y in the equation \[2x-3y=-2\] . Hence we get,
$\Rightarrow 2x-3\left( 24-4x \right)=-2$
Now using distributive property which says $a\left( b-c \right)=ab-ac$ we get,
$\begin{align}
  & \Rightarrow 2x-3\left( 24 \right)-3\left( -4x \right)=-2 \\
 & \Rightarrow 2x-72+12x=-2 \\
\end{align}$
Now transposing 72 on RHS and simplifying we get,
$\begin{align}
  & \Rightarrow 2x+12x=72-2 \\
 & \Rightarrow 14x=70 \\
\end{align}$
Now dividing the whole equation by 14 we get, x = 5.
Hence the value of x is 5.
Now substituting the value of x in $y=24-4x$ we get,
$\begin{align}
  & \Rightarrow y=24-4\left( 5 \right) \\
 & \Rightarrow y=24-20 \\
 & \Rightarrow y=4 \\
\end{align}$
Hence the value of y is 4.
Hence we get the solution of the equation is y = 4 and x = 5.

Note: Now note that here we have used the equation $4x+y=24$ for substitution. We can use any of the two given equations for substitution. Also in this problem we have written y in terms of x and then substituted the value of y. we can also write x in terms of y and substitute the value of x.