A Level 数学3.pptVIP

AS-Level Maths: Core 1for Edexcel C1.3 Algebra and functions 3 Encourage students to use substitution to check that the solutions x = 1 and y = 2 satisfy both equations. Ask students if they can think of a case where a pair of linear simultaneous equations will have no solutions. Establish that a pair of linear simultaneous equations will have no solutions if the graphs of their equations never intersect. The only time that two linear graphs never intersect is when they are parallel; that is, when they have the same gradient. This can be verified for a given pair of equations by arranging them both in the form y = mx + c and checking whether m is the same value in both equations. One more case is where both equations are actually the same but written in different forms. In this case, there are an infinite number of solutions corresponding to every point on the line. At this level, most examples will involve solving two equations with two unknowns. You may wish to make students aware that it is also possible to solve three simultaneous equations with three unknowns, four simultaneous equations with four unknowns, and so on. Point out that the x terms have the same number in front of them and the signs are the same. Subtracting the equations will eliminate the x terms. Tell students that it is usually sufficient to carry out this check mentally. In this example, the coefficient of y have a different sign and so we add the equations. Point out that we could also solve these equations by multiplying the first equation by 4, the second equation by 5 and subtracting them to eliminate x. In some examples, rearranging the equations into the form x = … or y = … may lead to equations involving fractions. Check mentally that these solutions are correct by substituting them into equation 2. Demonstrate the different number of roots possible by dragging the line through the parabola. Note that when the line touches the parabola at one point it forms a tangent to the curve. At