AI-generated answer
To solve the system of linear equations by graphing:
Given equations are:
1.
2.
To graph the first equation, , we can start by finding two points that lie on this line. Let's choose two x-values, say 0 and 4, and find the corresponding y-values:
For x = 0, . So, we have the point (0, 3).
For x = 4, . So, we have the point (4, 7).
Now, let's plot these points and draw a straight line passing through them. This line represents the equation on the graph.
To graph the second equation, , we can rewrite it in slope-intercept form:
Similarly, find two points that lie on this line:
For x = 0, . So, we have the point (0, 7).
For x = 4, . So, we have the point (4, 11).
Now, plot these points and draw a straight line passing through them. This line represents the equation on the graph.
After plotting both lines, we will notice that they intersect at a single point. This intersection point is the solution to the system of linear equations. Since there is only one point of intersection, the system of equations is consistent and independent, meaning it has a unique solution.
Therefore, the graph of the system of equations shows that the solution is a single point where the two lines intersect.
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