Find a solution to the system of equations by graphing Y equals 2X minus one and Y equals X +3
To find the solution to the system of equations by graphing, we will plot the graphs of both equations on the same coordinate plane and find the point where they intersect.
First, let's plot the graph of y = 2x - 1:
For this equation, we can choose any values for x and find the corresponding values for y. Let's choose three values for x: -1, 0, and 1.
When x = -1, y = 2(-1) - 1 = -2 - 1 = -3. So we have the point (-1, -3).
When x = 0, y = 2(0) - 1 = 0 - 1 = -1. So we have the point (0, -1).
When x = 1, y = 2(1) - 1 = 2 - 1 = 1. So we have the point (1, 1).
Now we can plot these points and draw the line passing through them:
The graph of y = 2x - 1 will look like this:
Now let's plot the graph of y = x + 3:
Following the same steps as above, we can choose three values for x: -2, 0, and 2.
When x = -2, y = -2 + 3 = 1. So we have the point (-2, 1).
When x = 0, y = 0 + 3 = 3. So we have the point (0, 3).
When x = 2, y = 2 + 3 = 5. So we have the point (2, 5).
Now we can plot these points and draw the line passing through them:
The graph of y = x + 3 will look like this:
To find the solution to the system of equations, we need to find the point of intersection of the two lines. From the graph, we can see that the lines 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 a solution to the system of equations by graphing, we can plot the graphs of both equations on the same coordinate plane and find the point where they intersect. This point represents the solution to the system.
The first equation is Y = 2X - 1, which is a linear equation with a slope of 2 and a y-intercept of -1. To graph this equation, we can start by plotting the y-intercept at -1 on the y-axis. Then, using the slope of 2, we can find another point by moving 1 unit to the right and 2 units up from the y-intercept. Draw a straight line passing through these two points to represent the graph of this equation.
The second equation is Y = X + 3, which is also a linear equation but with a slope of 1 and a y-intercept of 3. Similarly, we can plot the y-intercept at 3 on the y-axis and use the slope of 1 to find another point by moving 1 unit to the right and 1 unit up from the y-intercept. Draw a straight line passing through these two points to represent the graph of this equation.
Now, we can observe the graphed lines and find the point of intersection. This point represents the solution to the system of equations.