Question

How do you solve this system of equations \[2x-4y=-24\] and \[3x+4y=4\]?

Answer 1

Hint: To solve the system of equations in two variables, we need to follow the steps. The first step is to 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. After this, substitute this relationship in the other equation to get an equation in one variable. Now, solve this equation to find the solution value of the variable, and 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 \[2x-4y=-24\] and \[3x+4y=4\]. We know the steps required to solve a system of equations in two variables. Let’s take the first equation, we get
\[\Rightarrow 2x-4y=-24\]
Adding \[4y\] to both sides of equation, we get
\[\Rightarrow 2x=-24+4y\]
Dividing both sides by 2, we get
\[\Rightarrow x=-12+2y\]
Substituting this in the equation \[3x+4y=4\], we get
\[\Rightarrow 3\left( -12+2y \right)+4y=4\]
Simplifying the above equation, we get
\[\begin{align}
  & \Rightarrow -36+6y+4y=4 \\
 & \Rightarrow y=4 \\
\end{align}\]
Substituting this value in the relationship between variables to find the value of x, we get
\[\begin{align}
  & \Rightarrow x=-12+2(4) \\
 & \Rightarrow x=-4 \\
\end{align}\]
Hence, the solution values for the system of equations are\[x=-4\] and \[y=4\].

Note: We can also use the graphical method to solve this question. To do this, we first need to plot the graph of the two equations. As the equations are linear equations, their graph is a straight line. We will get two straight lines, the coordinates of their point of intersection are the solution of the system of equations. Thus, plotting the graph of the equations of a straight line,

The intersection point is the same as the solution we got.