Question

Find the solution to the system of equations by graphing Y = 3X - 1 and -3X + Y = -2

Answer 1

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.