Given a linear equation in x and y for example 3x + 2y = 1, [br]we can substitute random values of x and y, for example x = 1 and y = 1 to the left hand side,[br]to obtain 3(1) + 2(1) which adds to 5.[br]But this is not equal to 1, which is the right side of the equation.[br][b]So if the left side is not equal to the right side,[/b] [b]then the pair of x and y values we chose do not satisfy the condition that the left hand side must equal the right hand side of the equation.[/b][br][br]If x = 1 and y = -1 the 3(1) + 2(-1) = 1 which equals 1 on the right hand side of the equation[br]In this case, the pair of x and y values substituted into the left hand side of the equation, equals to the right hand side, and satisfies the condition of the equation.[br][br]Instead of randomly picking x and y values to satisfy the equation, we can actually substitute the value of x first and then obtain the value of y from the equation.[br]So for x = 1, we get 3(1) + 2y = 1[br] 2y = 1 -3[br] 2y = -2[br] y = -2/2 [br] y = -1[br]So x = 1 and corresponding value of y = -1 satisfy the equation as before[br][br]If x = 3, substituting it into the equation gives 3(3) + 2y = 1[br] 2y = 1-9[br] y = -8/2 = -4[br][br]So another pair of x, y values which satisfy the equation is x = 3, y = -4[br][br]These two pairs of x and y, together with numerous other pairs of x and y satisfying the equation can be plotted on a graph and it produces a straight line. [br][br]In the interactive resource below, a linear equation is presented, fill in the correct corresponding values of y and x for the given values of x and y.