To solve the given system of equations graphically, we need to plot the lines represented by each equation and find the point of intersection (if any).
1. Observe the first equation: x + 2y = 3.
To plot this line, rearrange the equation in terms of y:
2y = 3 - x
y = (3 - x)/2
Now, choose some values for x and calculate the corresponding values of y:
For x = 0, y = (3 - 0)/2 = 1.5
For x = 3, y = (3 - 3)/2 = 0
Plot the points (0, 1.5) and (3, 0) on the graph.
2. Observe the second equation: 2x + y = 0.
To plot this line, rearrange the equation in terms of y:
y = -2x
Choose some values for x and calculate the corresponding values of y:
For x = 0, y = 0
For x = 1, y = -2
Plot the points (0, 0) and (1, -2) on the graph.
Now, plot the two lines on the same graph and find their point of intersection, if any. Here is the graph:
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The two lines intersect at the point (1, -1). Thus, the solution to the system of equations is x = 1 and y = -1.
Solve the following pair of simultaneously equation graphically using gradient method
X+2y=3
2x+y=0
1 answer