find the solution to the system of equations by graphing y=3x -1 2x +y=4
To graph the system of equations y=3x - 1 and 2x + y = 4, we need to plot the lines represented by each equation on the coordinate plane and find the point of intersection.
For the first equation y=3x - 1, we can assign different values to x and calculate corresponding values for y. Let's choose x = 0, 1, and -1:
When x = 0, y = 3(0) - 1 = -1. So one point on the line is (0, -1).
When x = 1, y = 3(1) - 1 = 2. So another point on the line is (1, 2).
When x = -1, y = 3(-1) - 1 = -4. So another point on the line is (-1, -4).
Plotting these three points and connecting them, we get a line.
For the second equation, 2x + y = 4, we can also choose values for x and calculate corresponding values for y:
When x = 0, 2(0) + y = 4, y = 4. So one point on the line is (0, 4).
When x = 1, 2(1) + y = 4, y = 2. So another point on the line is (1, 2).
When x = -1, 2(-1) + y = 4, y = 6. So another point on the line is (-1, 6).
Plotting these three points and connecting them, we get another line.
Now, we can see where these two lines intersect. The point of intersection is (1, 2).
Therefore, the solution to the system of equations y=3x - 1 and 2x + y = 4 is x = 1 and y = 2.
To find the solution to the system of equations by graphing, we will plot the equations on a coordinate plane and determine the point(s) of intersection.
First, let's graph the first equation: y = 3x - 1.
To do this, we can choose a few values for x, calculate the corresponding y-values, and plot the points on the coordinate plane.
Let's start with x = 0:
y = 3(0) - 1
y = -1
So one point on the graph is (0, -1).
Now let's choose x = 1:
y = 3(1) - 1
y = 3 - 1
y = 2
So another point on the graph is (1, 2).
Plotting these two points and drawing a straight line passing through them:
```
|
3 + . (1, 2)
|
|
2 +
|
|
1 +
|
|
0 +-----+-----+
-1 1
(0, -1)
```
Next, let's graph the second equation: 2x + y = 4.
Again, we can choose values for x, calculate y-values, and plot the points.
For x = 0:
2(0) + y = 4
y = 4
So one point on the graph is (0, 4).
For x = 1:
2(1) + y = 4
2 + y = 4
y = 2
So another point on the graph is (1, 2).
Plotting these two points and drawing a straight line through them:
```
|
4 +
|
|
2 + . (1, 2)
|
|
0 +
|
|
-2 +-----+-----+
-1 1
(0, 4)
```
Now, we can see that the two lines intersect at the point (1, 2). This means that (1, 2) is the solution to the system of equations.
Therefore, the solution to the system of equations is x = 1 and y = 2.