Question

How do you solve the system by graphing: \[4x-2y=-12\] and \[2x+y=-2\]?

Answer 1

Hint: Find the points of where the lines will cut the two axes by substituting the value of x and y equal to 0 for each equation one by one. Join the two points to draw the graph of the lines considering one equation at a time. Now, check the point of intersection of the two lines and determine its coordinates to get the solution.

Complete step-by-step solution:
Here, we have been provided with the system of equations: - \[4x-2y=-12\] and \[2x+y=-2\] and we are asked to solve it using the graph.
Now, let us consider the two equations as: -
\[\Rightarrow 4x-2y=-12\] ------(1)
\[\Rightarrow 2x+y=-2\] -------(2)
Let us consider equation (1), so we have,
\[\Rightarrow 4x-2y=-12\]
Substituting x = 0, we get,
\[\begin{align}
  & \Rightarrow -2y=-12 \\
 & \Rightarrow y=6 \\
\end{align}\]
Substituting y = 0, we get,
\[\begin{align}
  & \Rightarrow 4x=-12 \\
 & \Rightarrow x=-3 \\
\end{align}\]
Therefore, the points where the line will cut the axes are: - A (0, 6) and B (-3, 0).
Let us consider equation (2), so we have,
\[\Rightarrow 2x+y=-2\]
Substituting x = 0, we get,
\[\Rightarrow y=-2\]
Substituting y = 0, we get,
\[\begin{align}
  & \Rightarrow 2x=-2 \\
 & \Rightarrow x=-1 \\
\end{align}\]
Therefore, the points where the line will cut the axes are: - C (0, -2) and D (-1, 0).
So, the graph of the two linear equations can be plotted as: -

From the above graph we can clearly see that the two straight lines are intersecting at point P whose coordinates are (-2, 2). So, point P (-2, 2) is the solution of the given system of equations.

Note: One may note that we can check our answer by solving the equations of the two given lines algebraically by using any of the three methods, i.e. substitution, elimination or cross - multiplication. If we will get the same coordinate of P as in the graph then our answer will be correct. It is not necessary to find the points where the lines cut the axes to draw the graph, you may take any other two points also but generally we substitute x and y equal to 0 because in these cases we do not have to perform any calculations to determine the points.