The graph of a linear equation ax+ by = c is a straight line equation.
Two distinct lines always intersect at exactly one point unless they are parallel (have the same slope).
The coordinates of the intersection point of the lines is the solution to the simultaneous linear equations describing the lines. So we would normally expect a pair of simultaneous equations to have just one solution.
Let's look at an example graphically:
2x + 3y = 7
4x + y = 9
From the graph we see that the point of intersection of the two lines is (2, 1)
Hence, the solution of the simultaneous equations is x = 2, y =1.
Two distinct lines always intersect at exactly one point unless they are parallel (have the same slope).
The coordinates of the intersection point of the lines is the solution to the simultaneous linear equations describing the lines. So we would normally expect a pair of simultaneous equations to have just one solution.
Let's look at an example graphically:
2x + 3y = 7
4x + y = 9
From the graph we see that the point of intersection of the two lines is (2, 1)
Hence, the solution of the simultaneous equations is x = 2, y =1.
