Question Solve the following system of linear equations by graphing. Graph on your own piece of paper. In your submitted answer, describe what the graph looks like and what this tells you about the solution to the system of linear equations. y=x+3 −4x+4y=28. step by step
To solve the system of linear equations by graphing, we need to graph the two equations on the same set of axes and find the point of intersection.
1. Let's start with the first equation y = x + 3. To graph this equation, we can make a table of values.
x | y
---------
-3 | 0
-2 | 1
-1 | 2
0 | 3
1 | 4
2 | 5
Plotting these points on a graph and connecting them, we get a straight line.
2. Now let's graph the second equation -4x + 4y = 28. To graph this equation, we need to rearrange it to the slope-intercept form.
-4x + 4y = 28
4y = 4x + 28
y = x + 7
Using the same table of values, we can plot the points.
x | y
---------
-3 | 4
-2 | 5
-1 | 6
0 | 7
1 | 8
2 | 9
Connecting these points, we get a second straight line.
3. Now that we have both lines graphed, we can observe the intersection point (where the lines cross).
The intersection point is (1, 4).
4. The graph of the two lines intersects at the point (1, 4). This means that (1, 4) is the solution to the system of linear equations.
The graph looks like two straight lines intersecting at a single point. This tells us that there is a unique solution to the system of linear equations.