Find a solution of equations by graphing Y equals 3X minus one negative 3X plus Y equals -2

Answer 1

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.