Solve the simultaneous equation by graphical method
1)3x_11=y;x_3y=9
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Good
Oh, I see you're trying to graphically solve a simultaneous equation. Sure, let me lend you a hand!
To graphically solve the equations 3x - y = 11 and x + 3y = 9, we need to plot the lines formed by each equation on a graph.
For the first equation 3x - y = 11, let's rearrange it to get y in terms of x:
y = 3x - 11. We can then form a table of values and plot the points:
x | y
--------------
0 | -11
2 | -5
4 | 5
Now, let's form the second equation x + 3y = 9:
3y = -x + 9
y = (-1/3)x + 3
Again, we form a table of values and plot the points:
x | y
--------------
0 | 3
3 | 2
6 | 1
Now that we have both lines plotted, let's look at the graph to find the point of intersection, which represents the solution to the simultaneous equations. Uh-oh, it seems that my clown nose gets smudged every time I try to draw graphs! Unfortunately, I can't really show you the graph, but I hope you get the idea.
The point where the two lines intersect is the solution to the simultaneous equation. In this case, the graph would show that x ≈ 2.5 and y ≈ -3.5.
So, according to my smudged graphs, the solution to the simultaneous equations 3x - y = 11 and x + 3y = 9 is approximately x = 2.5 and y = -3.5.
To solve the simultaneous equations by the graphical method, we need to graph both equations on the same coordinate plane and find the point where the two graphs intersect. This intersection point will represent the solution to the system of equations.
Let's solve the given equations step by step:
1) Equation 1: 3x - 11 = y
2) Equation 2: x + 3y = 9
To graph each equation, we need to rearrange them into the form y = mx + b, where m represents the slope and b represents the y-intercept.
For Equation 1:
Rearrange the equation: y = 3x - 11
To find the y-intercept: Set x = 0, solve for y: y = 3(0) - 11 = -11
To find the x-intercept: Set y = 0, solve for x: 0 = 3x - 11 -> 3x = 11 -> x = 11/3 ≈ 3.67
For Equation 2:
Rearrange the equation: x + 3y = 9 -> 3y = -x + 9 -> y = (-1/3)x + 3
To find the y-intercept: Set x = 0, solve for y: y = (-1/3)(0) + 3 = 3
To find the x-intercept: Set y = 0, solve for x: 0 = (-1/3)x + 9 -> (1/3)x = 9 -> x = 9 * 3 = 27
Now, we can plot the graphs of both equations on the same coordinate plane:
For Equation 1:
- Plot the y-intercept at (0, -11)
- Plot another point using the x-intercept at (3.67, 0)
- Draw a straight line passing through both points
For Equation 2:
- Plot the y-intercept at (0, 3)
- Plot another point using the x-intercept at (27, 0)
- Draw a straight line passing through both points
Now, we observe the point where the two lines intersect. The coordinates of that point represent the solution to the simultaneous equations.
By analyzing the graphs, it seems difficult to find the exact intersection point. However, we can make an educated estimate by observing the approximate coordinates of the intersection point.
It appears that the lines intersect at approximately (4, -2). Thus, a rough estimation of the solution to the simultaneous equations would be x ≈ 4 and y ≈ -2.
Please note that this solution is approximate since it is based on visual estimation. To obtain a more accurate solution, we can use other methods like substitution or elimination.
3 x -11 = y
what does that line look like?
if x = 0, y =-11 so mark (0,11)
if y = 0, x = 11/3 so mark (11/3 , 0)
etc
x - 3 y = 9 ??
3 x -11 = y
x - 3 y = 9 ??
I can not draw the lines but
3 x - 11 = y
3 x - 9 y = 27
------------------------ subtract
-11 + 9 y = y - 27
8 y = -16
y = -2
then
3 x - 11 = y
3 x - 11 = -2
3 x =9
x =3
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check
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x - 3 y = 9 ?
3 - 3(-2) = ?
3 + 6 = 9 sure enough