Find a solution of equations by graphing Y equals 3X minus one negative 3X plus Y equals -2
To find a solution of the equations by graphing, let's first plot the lines represented by each equation.
1) Equation 1: y = 3x - 1
2) Equation 2: -3x + y = -2
To plot the line represented by Equation 1, we can note that the equation is in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. Here, the slope (m) is 3, and the y-intercept (b) is -1. So, the line will pass through the point (0, -1), and we can use the slope to find additional points. For example, if we move one unit to the right (x + 1), we move three units up (y + 3). If we move one unit to the left (x - 1), we move three units down (y - 3). Plotting these points, we get:
Equation 1:
- Intercepts: (0, -1)
- Additional points: (1, 2) and (-1, -4)
To plot the line represented by Equation 2, we can rearrange it to slope-intercept form. Add 3x to both sides to isolate y:
Equation 2:
-3x + y = -2
y = 3x - 2
Now, we can identify the slope (m), which is also 3, and the y-intercept (b), which is -2. So, the line will pass through the point (0, -2), and using the slope, we find additional points:
Equation 2:
- Intercepts: (0, -2)
- Additional points: (1, 1) and (-1, -5)
Plotting the points and lines, we get:
Equation 1: y = 3x - 1 (in red)
Equation 2: y = 3x - 2 (in blue)
```
|
5 | . x x
| x
4 |
|
3 |
| x
2 | x
|
1 |
|
0 |________________
-2 -1 0 1
```
From the graph, we can observe that the two lines intersect at the point (1, 2). Therefore, the solution of the system of equations is x = 1 and y = 2.
To find a solution of the equations by graphing, we will plot the graphs of both equations and determine their point of intersection.
Let's start with the first equation:
Y = 3X - 1
To plot this equation, we need to find at least two points. We can select any values for X, calculate the corresponding Y values, and then plot the points on a graph. Let's choose X = 0 and X = 2.
When X = 0:
Y = 3(0) - 1
Y = -1
When X = 2:
Y = 3(2) - 1
Y = 5
So, we have two points: (0, -1) and (2, 5).
Now, let's move on to the second equation:
-3X + Y = -2
We can rearrange this equation to find Y in terms of X:
Y = 3X - 2
Again, let's select two values for X. Let's choose X = 0 and X = 2.
When X = 0:
Y = 3(0) - 2
Y = -2
When X = 2:
Y = 3(2) - 2
Y = 4
So, we have two points: (0, -2) and (2, 4).
Now, let's plot these points and draw the corresponding lines on a graph.
Once we have the graph, we can determine the point of intersection. This point will represent the solution to the system of equations.