solve the systems of equations by graphing
2x-y=1
8x-4y=+8
2X-Y=1. (0,-1), (1,1)
8X-4Y=8. (0,-2), (1,0)
The solution of the two equations is the point where their graphs intersect.
The graph using the above points showed that the lines are parallel and
do not intersect. Therefore. there is no solution. The two lines have equal
slopes which further proves that they are parallel. Slope1=-A/B=-2/-1=2, Slope2=-8/-4=2. If you solved the two equations mathematically using the
elimination method.the results will
be 0=4 which is not a true statement
and further proves that there is no
solution.
To solve the system of equations by graphing, we need to plot the lines represented by each equation and find the point where they intersect.
Let's start with the first equation, 2x - y = 1. To graph this equation, we need to rearrange it into slope-intercept form, which is y = mx + b, where "m" is the slope and "b" is the y-intercept.
Rearranging the equation, we get:
y = 2x - 1
To graph this line, we'll begin by plotting the y-intercept, which is -1, on the y-axis. Then, using the slope of 2, we can move up 2 units and over 1 unit to plot another point. We can continue this process to plot more points, or we can simply draw a straight line through the two points.
Now, let's move on to the second equation, 8x - 4y = 8. To graph this equation, we'll rearrange it into slope-intercept form.
Dividing both sides of the equation by 4, we get:
2x - y = 2
Rearranging further, we have:
y = 2x - 2
Just like before, we can plot the y-intercept, which is -2, and then use the slope of 2 to plot another point. Finally, we can draw a straight line through the two points.
Now that we have both lines graphed, we can find their point of intersection. This point represents the solution for the system of equations.
In this case, it appears that the two lines intersect at the point (1, 0). Therefore, the solution to the system of equations is x = 1 and y = 0.
To double-check this solution, you can substitute the values of x and y into both original equations to verify if they hold true.