Solve the following pair of simultaneously equation graphically using gradient method

X+2y=3
2x+y=0

1 answer

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.