Find the solution to the system of equations by graphing
Y=2x - 1 and y=x + 3
To graph the system of equations, first plot the y-intercept for each equation.
For the first equation, y = 2x - 1, the y-intercept is -1. Plot the point (0, -1).
For the second equation, y = x + 3, the y-intercept is 3. Plot the point (0, 3).
Next, find the slope for each equation.
The slope for the first equation, y = 2x - 1, is 2. This means that for every 1 unit increase in x, the corresponding y-value increases by 2.
The slope for the second equation, y = x + 3, is 1. This means that for every 1 unit increase in x, the corresponding y-value increases by 1.
Plot the slope by moving up 2 units and over 1 unit from the first point. Then plot the slope by moving up 1 unit and over 1 unit from the second point. Repeat this process to plot additional points.
The graph of the two equations should intersect at a single point. This point represents the solution to the system of equations.
To find the solution to the system of equations by graphing, we need to graph both equations on the same coordinate plane.
First, let's graph the equation y = 2x - 1. To do this, we will plot a few points and then draw a line through them.
Let's choose some x-values and find the corresponding y-values:
For x = 0, y = 2(0) - 1 = -1. So we have the point (0, -1).
For x = 1, y = 2(1) - 1 = 1. So we have the point (1, 1).
Plotting these points and drawing a line through them, we get:
```
|
3 |
| .
2 |
| .
1 |
| .
0 |
|_________
1 2 3
```
Next, let's graph the equation y = x + 3. Again, we'll plot a couple of points and draw a line through them.
For x = 0, y = 0 + 3 = 3. So we have the point (0, 3).
For x = 1, y = 1 + 3 = 4. So we have the point (1, 4).
Plotting these points and drawing a line through them, we get:
```
| .
4 |
| .
3 |
| .
2 |
| .
1 |
| .
0 |
|_________
1 2 3
```
Now, we can visually see where the two lines intersect, which represents the solution to the system of equations.
From the graph, we can see that the two lines intersect at the point (2, 5). Therefore, the solution to the system of equations y = 2x - 1 and y = x + 3 is x = 2 and y = 5.
I hope this helps! Let me know if you have any more questions.