Page 33 - Algebra
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2.8. System of Equations
From the above chapters, recall the system of linear equations in two variables. 5x – 3y = 6
4x + 5y = 12
Now, let us use x = 3 and y = 3 in the LHS of the first equation. 5(3) – 3(3) = 15 – 9 = 6
Here, LHS = RHS
So, (3, 3) is a solution of 5x – 3y = 6
Put (4, 2) in the first equation 5(4) – 3(2)
= 20 – 6 = 14
Here, LHS ≠ RHS
So, (4, 2) is not a solution of 5x – 3y = 6
From the above two, it’s clear that point (3, 3) lies on the line 5x - 3y = 6, but the point (4, 2) does not lie on 4x + 5y = 12.
This implies that every point which lies on the line ax + by = c, is a solution to the equation.
When you graphically plot two equations on the Cartesian plane, one of the following possibilities can happen.
• The lines intersect at a point,
• The lines do not intersect and are parallel to each other,
• The two lines are coincident.
Page 32 of 177
Algebra I & II
