Use graphical method to solve the simultaneous equation 2x+y=1 and 4x+y=-3
To solve the simultaneous equations 2x + y = 1 and 4x + y = -3 graphically, we need to plot the lines represented by each equation on a coordinate plane and determine the point of intersection.
First, we rearrange each equation to solve for y:
Equation 1: 2x + y = 1
y = -2x + 1
Equation 2: 4x + y = -3
y = -4x - 3
Next, we can create a table of values for each equation:
Equation 1:
x | y
-------
0 | 1
1 | -1
2 | -3
Equation 2:
x | y
--------
0 | -3
1 | -7
2 | -11
Plotting these points and drawing lines through them, we get the following graph:
| .
| .
| .
-11 |_____________________________
| .
| .
| .
-7 |______________________
| .
| .
| .
-3 |______________
| .
| .
| .
|_________
0 1 2 3 4
The lines intersect at coordinates (-2, 5/2) or (-2, 2.5). Therefore, the solution to the system of equations is x = -2 and y = 2.5.
To solve the simultaneous equations graphically, we will plot the two equations on the Cartesian plane and find the point of intersection. Let's solve the equations 2x + y = 1 and 4x + y = -3 step-by-step:
Step 1: Convert the equations to slope-intercept form (y = mx + b):
1) 2x + y = 1
y = -2x + 1
2) 4x + y = -3
y = -4x - 3
Step 2: Plot the two lines on a graph.
The line represented by y = -2x + 1 has a slope of -2 and a y-intercept of 1. Start by plotting the y-intercept at (0, 1), and then use the slope to find another point. For example, if x = 1, then y = -2(1) + 1 = -1. Plot this point as well.
The line represented by y = -4x - 3 has a slope of -4 and a y-intercept of -3. Start by plotting the y-intercept at (0, -3), and then use the slope to find another point. For example, if x = 1, then y = -4(1) - 3 = -7. Plot this point as well.
Step 3: Find the point of intersection.
From the graph, we can see that the lines intersect at the point (-1, 3). This represents the solution to the simultaneous equations.
Therefore, the solution to the simultaneous equations 2x + y = 1 and 4x + y = -3 is x = -1 and y = 3.
To solve the simultaneous equations 2x + y = 1 and 4x + y = -3 using the graphical method, we can plot the equations on a coordinate plane and find the point of intersection, which represents the solution to the equations. Here's how you can do it step by step:
Step 1: Rearrange each equation to solve for y in terms of x:
Equation 1: 2x + y = 1 => y = 1 - 2x
Equation 2: 4x + y = -3 => y = -3 - 4x
Step 2: Choose a range of values for x and substitute them into each equation to determine the corresponding values of y. You can select a range of x-values such as -5 to +5.
Step 3: Now, plot the points that you obtained from the substitutions on the coordinate plane. Each point represents a solution that satisfies both equations.
Step 4: Draw a straight line through the points for each equation. These lines represent the graph of each equation.
Step 5: Identify the point where the two lines intersect. This point represents the solution to the simultaneous equations.
Step 6: Read the coordinates of the point of intersection. The x-coordinate and y-coordinate of the point represent the values that satisfy both equations simultaneously, giving you the solution to the simultaneous equations.
By following these steps, you can graphically solve the simultaneous equations 2x + y = 1 and 4x + y = -3.