Find the solution to the system of equations by graphing why equals 2X - 1 and y=x+3
To find the solution to the system of equations y = 2x - 1 and y = x + 3 by graphing, we can plot the graphs of these equations on the same coordinate plane and identify the point of intersection.
First, we'll graph the equation y = 2x - 1:
To do this, we'll choose a range of x-values and then plot the corresponding y-values using the equation y = 2x - 1. For simplicity, we'll choose x-values ranging from -2 to 2.
When x = -2, y = 2(-2) - 1 = -4 - 1 = -5. So, one point on the graph is (-2, -5).
When x = -1, y = 2(-1) - 1 = -2 - 1 = -3. So, another point on the graph is (-1, -3).
When x = 0, y = 2(0) - 1 = 0 - 1 = -1. So, another point on the graph is (0, -1).
When x = 1, y = 2(1) - 1 = 2 - 1 = 1. So, another point on the graph is (1, 1).
When x = 2, y = 2(2) - 1 = 4 - 1 = 3. So, another point on the graph is (2, 3).
Plotting these points and connecting them, we get a straight line. Let's label this line as Line A.
Next, we'll graph the equation y = x + 3:
Again, we'll choose a range of x-values and then plot the corresponding y-values using the equation y = x + 3. We'll use the same range of x-values as before.
When x = -2, y = -2 + 3 = 1. So, one point on the graph is (-2, 1).
When x = -1, y = -1 + 3 = 2. So, another point on the graph is (-1, 2).
When x = 0, y = 0 + 3 = 3. So, another point on the graph is (0, 3).
When x = 1, y = 1 + 3 = 4. So, another point on the graph is (1, 4).
When x = 2, y = 2 + 3 = 5. So, another point on the graph is (2, 5).
Plotting these points and connecting them, we get another straight line. Let's label this line as Line B.
Now, we can observe the intersection point of Line A and Line B.
From the graph, it can be seen that Line A and Line B intersect at the point (2, 5).
Therefore, the solution to the system of equations y = 2x - 1 and y = x + 3 is x = 2 and y = 5.
To find the solution to the system of equations, we can graph the equations and find the point of intersection. The point where both equations intersect is the solution to the system.
Let's start by graphing the two equations on the same coordinate system:
Equation 1: y = 2x - 1
Equation 2: y = x + 3
To graph Equation 1, we can start by finding two points on the line by substituting values for x and solving for y. For example, when x = 0, y = 2(0) - 1 = -1. This gives us the point (0, -1). Similarly, when x = 1, y = 2(1) - 1 = 1. This gives us the point (1, 1).
For Equation 2, we can follow the same process. When x = 0, y = 0 + 3 = 3. This gives us the point (0, 3). When x = -1, y = -1 + 3 = 2. This gives us the point (-1, 2).
Plotting these points on the graph, we have:
Equation 1: y = 2x - 1 (points: (0, -1) and (1, 1))
Equation 2: y = x + 3 (points: (0, 3) and (-1, 2))
Now draw a line through these points on the graph.
The intersection point of both lines is the solution to the system of equations. In this case, it appears that the two lines intersect at the point (-1, 2).
Therefore, the solution to the system of equations is x = -1 and y = 2.