Solve the simultaneous equation using graphical method 2y-x=4 and 2y+x=6
To solve the simultaneous equation using the graphical method, we can plot the graphs of the two equations and find the point of intersection, which represents the solution.
The given equations are:
1) 2y - x = 4
2) 2y + x = 6
Rearranging equation 1) to solve for y:
2y = x + 4
y = (1/2)x + 2
Rearranging equation 2) to solve for y:
2y = -x + 6
y = (-1/2)x + 3
Now we can plot the graphs of these equations:
The graph of equation 1) is a straight line with a slope of 1/2 and a y-intercept at (0, 2).
The graph of equation 2) is a straight line with a slope of -1/2 and a y-intercept at (0, 3).
Graphing these two equations will give us two lines:
The graph of equation 1) (in blue) will pass through the points (0, 2) and (4, 4).
The graph of equation 2) (in red) will pass through the points (0, 3) and (6, 0).
Now, we can see from the graph that the two lines intersect at the point (2, 3).
Therefore, the solution to the simultaneous equation is x = 2 and y = 3.
Graph:
https://www.desmos.com/calculator/jzymw7o2mm
To solve the simultaneous equations 2y - x = 4 and 2y + x = 6 using the graphical method, follow these steps:
Step 1: Rearrange the equations to isolate y:
- Equation 1: 2y - x = 4
Add x to both sides: 2y = x + 4
Divide by 2: y = (1/2)x + 2
- Equation 2: 2y + x = 6
Subtract x from both sides: 2y = -x + 6
Divide by 2: y = (-1/2)x + 3
Step 2: Plot the graphs of both equations on the same coordinate system. To do this, choose several values for x and substitute them into the equations to find the corresponding values of y. Then, plot the points (x, y) on the graph.
Step 3: Find the solution by identifying the point where the two graphs intersect. This point represents the values of x and y that satisfy both equations simultaneously.
Now, let's plot the graphs:
- Equation 1: y = (1/2)x + 2
Choose a few values for x:
When x = 0, y = (1/2)(0) + 2 = 2
When x = 2, y = (1/2)(2) + 2 = 3
When x = -2, y = (1/2)(-2) + 2 = 1
Plot the points (0, 2), (2, 3), and (-2, 1) on the graph.
- Equation 2: y = (-1/2)x + 3
Choose a few values for x:
When x = 0, y = (-1/2)(0) + 3 = 3
When x = 2, y = (-1/2)(2) + 3 = 2
When x = -2, y = (-1/2)(-2) + 3 = 4
Plot the points (0, 3), (2, 2), and (-2, 4) on the same graph.
Step 4: Identify the point of intersection on the graph. The coordinates of this point represent the solution to the simultaneous equations.
To solve the simultaneous equations 2y - x = 4 and 2y + x = 6 using the graphical method, follow these steps:
1. Rewrite the equations in slope-intercept form (y = mx + b):
Equation 1: 2y - x = 4 => y = (1/2)x + 2
Equation 2: 2y + x = 6 => y = (-1/2)x + 3
2. Plot the points on a graph:
Equation 1: y = (1/2)x + 2
For x = 0, y = 2, giving point (0, 2)
For x = 4, y = 4, giving point (4, 4)
Plot these points and draw a line connecting them.
Equation 2: y = (-1/2)x + 3
For x = 0, y = 3, giving point (0, 3)
For x = 6, y = 0, giving point (6, 0)
Plot these points and draw a line connecting them.
3. Determine the point of intersection:
The point where the two lines intersect is the solution to the simultaneous equations. Using the graph, you can see that the point of intersection is (2, 3).
Therefore, the solution to the simultaneous equations 2y - x = 4 and 2y + x = 6 is x = 2 and y = 3.