Find the solution to the system of equations by graphing Y = 3X - 1 and -3X + Y = -2
To graph the system of equations, we can rewrite them in slope-intercept form:
1) Y = 3X - 1
2) -3X + Y = -2 --> Y = 3X - 2
Now we can start by graphing the first equation:
For equation 1), we can see that the y-intercept is -1, and the slope is 3/1. We can use this information to plot two points on the graph. Let's say, when X = 0, Y = -1. When X = 1, Y = 2.
For equation 2), we can see that the y-intercept is -2, and the slope is 3/1. Similarly, we can plot two points. Let's say, when X = 0, Y = -2. When X = 1, Y = 1.
Graphing these points and connecting them with a line, we get:
{{{graph(400, 400, -5, 5, -5, 5, 3x-1, 3x-2)}}}
The solution to the system of equations is the point where the two lines intersect. From the graph, we can see that the lines intersect at (1, 2). Thus, the solution to the system of equations is X = 1 and Y = 2.
To solve the system of equations by graphing, we will plot the equations on a graph and find the intersection point. The intersection point will provide the solution to the system.
Let's start with the first equation, Y = 3X - 1.
We can choose some values for X and calculate the corresponding values of Y to create a table of values. Let's substitute X with -1, 0, and 1.
When X = -1:
Y = 3(-1) - 1
Y = -3 - 1
Y = -4
When X = 0:
Y = 3(0) - 1
Y = 0 - 1
Y = -1
When X = 1:
Y = 3(1) - 1
Y = 3 - 1
Y = 2
Now, let's plot these points on a graph. The points are (-1, -4), (0, -1), and (1, 2).
Next, let's graph the second equation, -3X + Y = -2.
To graph this equation, we need to rearrange it to the slope-intercept form, Y = MX + B.
-3X + Y = -2 can be rewritten as Y = 3X - 2.
Substituting X with -1, 0, and 1, we can find the corresponding values of Y.
When X = -1:
Y = 3(-1) - 2
Y = -3 - 2
Y = -5
When X = 0:
Y = 3(0) - 2
Y = 0 - 2
Y = -2
When X = 1:
Y = 3(1) - 2
Y = 3 - 2
Y = 1
Now, let's plot these points on the graph. The points are (-1, -5), (0, -2), and (1, 1).
Plotting both equations on the graph, we can see that they intersect at the point (1, 2).
Therefore, the solution to the system of equations is X = 1 and Y = 2.