Question

How do you solve the system of linear equations $4x+3y=-2$ and $2x-2y=-8$ ?

Answer 1

Hint: Now we are given with two linear equations $4x+3y=-2$ and $2x-2y=-8$ . Now we want to find the solution of the linear equation. To find the solution we will use the method of substitution. In this method we will try to express x in terms of y. Hence we have the value of x in terms of y. Now we will substitute this value in another equation and find the value of y. Now substituting this value of y in any equation we will get the value of x.

Complete step by step solution:
Now we are given with two equations $4x+3y=-2$ and $2x-2y=-8$
Now we know that the given equations are linear equations in two variables. To solve the equation we will use a method of substitution.
Let us first consider the second equation $2x-2y=-8$ .
Now rearranging the terms by transposing 2y on RHS we get,
$\Rightarrow 2x=2y-8$
Now dividing the equation by 2 we get,
$\Rightarrow x=y-4$
Now we have the value of x in terms of y.
Now substituting $x=y-4$ in the equation $4x+3y=-2$ we get,
$\begin{align}
  & \Rightarrow 4\left( y-4 \right)+3y=-2 \\
 & \Rightarrow 4y-16+3y=-2 \\
 & \Rightarrow 7y=16-2 \\
 & \Rightarrow 7y=14 \\
\end{align}$
Now dividing the whole equation by 7 we get $y=2$ .
Hence we have the value of y is 2.
Now let us substitute y = 2 in the equation $x=y-4$ hence we get,
$\begin{align}
  & \Rightarrow x=2-4 \\
 & \Rightarrow x=-2 \\
\end{align}$
Hence we get the value of x = -2.

Hence the value of x and y is -2 and 2 respectively.

Note: Now note that in method of substitution we can also write y in terms of x. Now while substituting the equation always remember to substitute the equation in another equation which is not used before. Once we have the value of one variable, we can substitute it in any equation to get the value of another variable.