Question

How do you solve the system by graphing: \[3x+4y=12\] and \[2x+4y=8\]?

Answer 1

Hint: Draw the graph of the two given equations. To draw the graph of a straight line, we need at least two points. So, choose one of the equations and substitute x = 0, determine y, then substitute y = 0, determine x. Now, apply the same process for the second equation. Plot the graph of the two equations using the points obtained. Check the point of intersection to get the answer.

Complete step-by-step solution:
Here, we have been provided with the system of equations: - \[3x+4y=12\] and \[2x+4y=8\] and we are asked to solve it using the graph.
Now, let us consider the two equations are: -
\[\Rightarrow 3x+4y=12\] - (1)
\[\Rightarrow 2x+4y=8\] - (2)
Let us consider equation (1), so we have,
\[\Rightarrow 3x+4y=12\]
Substituting x = 0, we get,
\[\begin{align}
  & \Rightarrow 4y=12 \\
 & \Rightarrow y=3 \\
\end{align}\]
Substituting y = 0, we get,
\[\begin{align}
  & \Rightarrow 3x=12 \\
 & \Rightarrow x=4 \\
\end{align}\]
Therefore, the points where the line cut the axes are: - A (0, 3) and B (4, 0).
Let us consider equation (2), so we have,
\[\Rightarrow 2x+4y=8\]
Substituting x = 0, we get,
\[\begin{align}
  & \Rightarrow 4y=8 \\
 & \Rightarrow y=2 \\
\end{align}\]
Substituting y = 0, we get,
\[\begin{align}
  & \Rightarrow 2x=8 \\
 & \Rightarrow x=4 \\
\end{align}\]
Therefore, the points where the line will cut the axes are: - C (0, 2) and D (4, 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 B or D both of whose coordinates are (4, 0). So, point B or D 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. If we will get the value of x and y similar to the obtained coordinates of P then it means that our answer is correct. Remember that while drawing the graph, substitute x = 0 and y = 0 to determine the points. If we will use any other values of x and y then we will have to do some calculations to draw the graph. Do not forget to draw and mark important points on the graph like the points where the lines cut the axes.