Solve this pair of equations by the graphical method: 4x+y=9 , 3y-2y=49
It's difficult to show here the graphical method, but there are many ways on how to do this.
One way is to choose three random values of x (for example, 0, 1, and 2) and get the corresponding y value by substituting these values to both equations, and plot the points on a graphing paper.
The other is to get the x- and y-intercepts of both equation, and plot them on a graphing paper.
In any case, you just have to find the point of intersection of the equations (if they are intersecting lines). Note that if they happen to be parallel, there is no solution (because no intersecting point), and if coinciding lines, they have infinite solutions.
Hope this helps~ :)
Here is a very useful webpage that can do what you asked for
First change each equation to function form, ie
y = 9-4x and y = (3x-49)/2
enter 9-4x in 1st graph and (3x-49)/2 into second graph, hit draw
http://rechneronline.de/function-graphs/
at first you can't see the solution, so change the
"range of x" and range of y values
(I entered x's from 5.8 to 6.6
and the y's from -16 to -13 to get a pretty good look at the solution)
btw, notice entering the y's from smallest to highest is consistent with the input for x's
x+2y=9
2x-4y=2
To solve the given pair of equations by the graphical method, we need to plot the graphs of both equations on the same coordinate system and find the point of intersection.
Let's solve the equations step by step:
1. Equation 1: 4x + y = 9
To plot this equation, we need to rearrange it in terms of y:
y = 9 - 4x
By substituting different values of x, we can find corresponding values of y. Here are a few points:
(0, 9)
(2, 1)
(4, -7)
Plot these points on a coordinate system and draw a straight line passing through them. This line represents Equation 1.
2. Equation 2: 3y - 2x = 49
Rearranging it in terms of y, we have:
y = (49 + 2x)/3
Using different values of x, we can find the corresponding y-values. Here are a few points:
(0, 49/3)
(3, 53/3)
(6, 57/3)
Plot these points on the same coordinate system and draw a straight line passing through them. This line represents Equation 2.
Now, analyze the graph and locate the point where the two lines intersect. This point represents the solution to the system of equations.
In this case, the lines do not intersect, indicating that there is no solution to the system of equations. The equations are parallel, and their lines will never cross each other.
Hence, there is no solution to this pair of equations.