Question

How do you solve the system by graphing: \[x-y=5\] and \[x+y=3\]?

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: \[x-y=5\] and \[x+y=3\] and we are asked to solve them graphically.
Now, let us assume consider the two equations as: -
\[\Rightarrow x-y=5\] - (1)
\[\Rightarrow x+y=3\] - (2)
Let us consider equation (1), so we have,
\[\Rightarrow x-y=5\]
Substituting y = 0, we get,
\[\Rightarrow x=5\]
Substituting x = 0, we get,
\[\begin{align}
  & \Rightarrow -y=5 \\
 & \Rightarrow y=-5 \\
\end{align}\]
Therefore, the two points where the line will cut the two axes are: - A (0, -5) and B (5, 0).
Let us consider equation (2), so we have,
\[\Rightarrow x+y=3\]
Substituting x = 0, we get,
\[\Rightarrow y=3\]
Substituting y = 0, we get,
\[\Rightarrow x=3\]
Therefore, the points where the line will cut the axes are: - C (0, 3) and D (3, 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 coordinate is (4, -1). So, point P (4, -1) is the solution of the given system of equations.

Note: If you want to check if we have obtained the correct point as the solution or not then substitute the coordinates in the given equation, if it satisfies both the equations then our answer is correct otherwise not. Remember that while drawing the graph, substitute x = 0 and y = 0 to determine the points or you may have to perform some calculations to draw the graph. Do not forget to mark important points on the graph like the points where the lines cut the axes.