Question

How do you solve this system of equations \[-4x-2y=-12\] and \[4x+8y=24\]?

Answer 1

Hint: To solve the system of equations in two variables, we need to follow the steps given below in the same order:
Step 1: choose one of the equations to find the relationship between the two variables. This can be done by taking one of the variables to the other side of the equation.
Step 2: substitute this relationship in the other equation to get an equation in one variable.
Step 3: solve this equation to find the solution value of the variable.
Step 4: substitute this value in any of the equations to find the value of the other variable.

Complete step by step solution:
We are given the two equations \[-4x-2y=-12\] and \[4x+8y=24\]. We know the steps required to solve a system of equations in two variables. Let’s take the first equation, we get
\[\Rightarrow -4x-2y=-12\]
Adding \[2y\] to both sides of equation, we get
\[\Rightarrow -4x=-12+2y\]
Multiplying both sides by \[-1\], we get
\[\Rightarrow 4x=12-2y\]
Substituting this in the equation \[4x+8y=24\], we get
\[\Rightarrow 12-2y+8y=24\]
Simplifying the above equation, we get
\[\Rightarrow y=2\]
Substituting this value in the relationship between variables to find the value of x, we get
\[\Rightarrow 4x=12-2(2)=8\]
Dividing both sides by 4 to above equation, we get
\[\Rightarrow x=2\]
Hence, the solution values for the system of equations are \[x=y=2\].

Note: Here the coefficient of x in both equations is of opposite signs, so we can also solve this problem as,
Adding the given equations, we get
\[\begin{align}
  & \Rightarrow -4x-2y+4x+8y=-12+24 \\
 & \Rightarrow 6y=12 \\
 & \Rightarrow y=2 \\
\end{align}\]
Substituting this value in the first equation, we get
\[\begin{align}
  & \Rightarrow -4x-2(2)=-12 \\
 & \Rightarrow -4x=-8 \\
\end{align}\]
Dividing both sides of above equation by 2, we get
\[\Rightarrow x=2\]