To graph the system of linear equations, we can start by graphing each equation separately.
For the first equation, y = x + 3, we can simply plot a few points to draw a line. Let's choose x = 0, x = 1, and x = -1.
When x = 0, y = 0 + 3 = 3.
When x = 1, y = 1 + 3 = 4.
When x = -1, y = -1 + 3 = 2.
Plotting these points, we get a line that passes through (0, 3), (1, 4), and (-1, 2). This line has a positive slope and goes up from left to right.
For the second equation, -4x + 4y = 28, let's solve for y in terms of x.
-4x + 4y = 28
4y = 4x + 28
y = x + 7
Similarly, we can plot a few points to draw a line. Let's choose x = 0, x = 1, and x = -1.
When x = 0, y = 0 + 7 = 7.
When x = 1, y = 1 + 7 = 8.
When x = -1, y = -1 + 7 = 6.
Plotting these points, we get a line that passes through (0, 7), (1, 8), and (-1, 6). This line also has a positive slope and goes up from left to right.
Now, we can observe the graph. The two lines intersect at the point (2, 5). This point represents the solution to the system of linear equations.
Based on the graph, we can conclude that the solution to the system of linear equations is x = 2 and y = 5.
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
7 answers
so, (2, 5)?
Yes, that is correct. The point of intersection of the two lines is (2, 5). Therefore, the solution to the system of linear equations is x = 2 and y = 5.
describe what the graph looks like and what this tells you about the solution to the system of linear equations.
The graph of the system of linear equations consists of two lines. Both lines have a positive slope and go up from left to right.
The first line, y = x + 3, passes through the point (0, 3) and increases by one unit in both the x and y directions.
The second line, y = x + 7, passes through the point (0, 7) and also increases by one unit in both the x and y directions.
The lines intersect at the point (2, 5), which means that x = 2 and y = 5 is the solution to the system of linear equations. This point represents the coordinates where the two lines meet and satisfy both equations simultaneously.
In other words, the solution to the system indicates that for x = 2, y = 5 satisfies both equations. The graphical representation visually confirms this by showing the point of intersection.
The first line, y = x + 3, passes through the point (0, 3) and increases by one unit in both the x and y directions.
The second line, y = x + 7, passes through the point (0, 7) and also increases by one unit in both the x and y directions.
The lines intersect at the point (2, 5), which means that x = 2 and y = 5 is the solution to the system of linear equations. This point represents the coordinates where the two lines meet and satisfy both equations simultaneously.
In other words, the solution to the system indicates that for x = 2, y = 5 satisfies both equations. The graphical representation visually confirms this by showing the point of intersection.
Where do these points end and start?
Apologies for any confusion. The lines extend infinitely in both directions on the graph. The points (0, 3), (1, 4), (2, 5), and so on, are just a few points on the line y = x + 3. Similarly, the points (0, 7), (1, 8), (2, 9), and so on, are just a few points on the line y = x + 7.
The lines never truly "start" or "end" on the graph, as they continue indefinitely in both directions. The points mentioned are just specific points that lie on the lines to help us understand their direction and slope.
The lines never truly "start" or "end" on the graph, as they continue indefinitely in both directions. The points mentioned are just specific points that lie on the lines to help us understand their direction and slope.
1 answer