Question

How do you solve this system of equations \[x-0.6x+0.4y=4\] and \[0.4x+2.4y=-8\]?

Answer 1

Hint: Here, we are given two linear equations in two variables. The first equation is \[x-0.6x+0.4y=4\], as we can see that this equation has two terms of x in the left side of the equation. On simplifying we get, \[0.4x+0.4y=4\]. The second equation is \[0.4x+2.4y=-8\]. The coefficients of x in the first and second equation are same. Thus, if we subtract the equation from each other, we can get rid of terms of variable x and we will get a linear equation in one variable. On solving this equation, we will get the solution value of y. using this value, we can find the solution value for x. This is easier to solve compared to the standard steps.

Complete step by step solution:
We are given a system of linear equations in two variables. The first equation is \[x-0.6x+0.4y=4\], as we can see that this equation has two terms of x in the left side of the equation. On simplifying we get, \[0.4x+0.4y=4\]. The second equation is \[0.4x+2.4y=-8\].
As we can see that the coefficient of x in both equations is the same. We can solve the given problem as follows,
Subtracting the second equation from the first, we get
\[\Rightarrow 0.4x+0.4y-\left( 0.4x+2.4y \right)=4-\left( -8 \right)\]
Simplifying the above equation, we get
\[\Rightarrow -2y=12\]
Dividing the above equation by \[-2\], and cancelling out the common factors, we get
\[\Rightarrow y=-6\]
Substituting this value in the first equation, we get
\[\Rightarrow 0.4x+0.4(-6)=4\]
Simplifying the above equation, we get
\[\Rightarrow 0.4x-2.4=4\]
Solving the above equation, we get
\[\Rightarrow x=16\]

Hence, the solution values for the system of equations are \[x=16\And y=-6\].

Note: We will now use the standard steps to solve this system of equations. The first equation is,
\[\begin{align}
  & \Rightarrow x-0.6x+0.4y=4 \\
 & \Rightarrow 0.4x+0.4y=4 \\
\end{align}\]
Subtracting \[0.4y\]from both sides of equation, we get
\[\Rightarrow 0.4x=4-0.4y\]
Substituting this in the equation \[0.4x+2.4y=-8\], we get
\[\Rightarrow 4-0.4y+2.4y=-8\]
Simplifying the above equation, we get
\[\Rightarrow 2y=-12\]
Dividing both sides of above equation by 2, we get
\[\Rightarrow y=-6\]
To find the value of x, we get
\[\begin{align}
  & \Rightarrow 0.4x=4-0.4(-6) \\
 & \Rightarrow 0.4x=4+2.4=6.4 \\
\end{align}\]
Dividing both sides of the above equation by \[0.4\], we get
\[\Rightarrow x=16\]