Find the solution to the system of equations by graphing Y equals 3X minus one negative 3X plus Y equals -2
To find the solution to the system of equations by graphing, we need to graph the two equations on the same coordinate plane and find the point at which they intersect.
First, let's graph the equation y = 3x - 1:
We can start by finding the x and y-intercepts of the equation.
For the x-intercept, we set y = 0 and solve for x:
0 = 3x - 1
1 = 3x
x = 1/3
So the x-intercept is (1/3, 0).
For the y-intercept, we set x = 0 and solve for y:
y = 3(0) - 1
y = -1
So the y-intercept is (0, -1).
Plot these two points on the coordinate plane and draw a line passing through them. This line represents the equation y = 3x - 1.
Next, let's graph the equation -3x + y = -2:
To graph this equation, we can rewrite it in slope-intercept form (y = mx + b) by isolating y:
-3x + y = -2
y = 3x - 2
This equation has the same slope (3) as the first equation, but a different y-intercept (-2 instead of -1).
Plot the y-intercept of the second equation, which is (0, -2), and draw a line passing through this point with a slope of 3.
Now, examine the graph:
The two lines representing the equations intersect at a single point, which is the solution to the system of equations. The coordinates of this point are the x-coordinate and y-coordinate of the intersection.
By visually inspecting the graph, we can estimate that the intersection point is approximately (1, 2).
Therefore, the solution to the system of equations is x = 1 and y = 2.
To solve the system of equations graphically, we will graph both equations on the same coordinate plane and find the point of intersection, which represents the solution.
The first equation is Y = 3X - 1, which is in slope-intercept form (Y = mx + b) with a slope of 3 and a y-intercept of -1. To graph this equation, we can start at the y-intercept of -1 and then use the slope of 3 to find another point. Let's plot these points and draw the line:
(Note: The points are approximate due to the limitations of text-based response)
Point A: (0, -1)
Point B: (1, 2)
Drawing the line passing through these two points, we get:
----- Line 1 -----
The second equation is -3X + Y = -2, which can be rearranged to Y = 3X - 2 by adding 3X to both sides. This equation is also in slope-intercept form with a slope of 3 but a y-intercept of -2. Let's plot the points and draw the line:
Point C: (0, -2)
Point D: (1, 1)
Drawing the line passing through these two points, we get:
----- Line 2 -----
Now, we can observe that both lines intersect at a common point. This point represents the solution to the system of equations.
By examining the graph, we can approximate the point of intersection as (1, 2).
Therefore, the solution to the system of equations is X = 1 and Y = 2.