Mathematics grade 10
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This document provides instructions on solving simultaneous equations in three main steps: 1) using elimination or substitution to remove one variable and solve for the other, 2) determining the intersection point of two graphs, and 3) working through two examples that apply these steps. The examples calculate two resistances given their sum and difference, and find the points where two equations for x^2 + y^2 and y = -3x - 5 intersect. References for further information are also included.
Mathematics grade 10
- 2. To solve two simultaneous equations means to use both equations together to find one value for each unkown so that these values satisfy both equations.
- 3. Steps to solve a quadratic equation. Move all terms to the LHS leaving only a zero on the RHS Factorise the LSH Use the zero-factor principle to find the values of variables
- 4. Methods to solve simultaneous equations. By elimination of one variable By substituting By determining the intersection point of two graphs.
- 5. Example. The sum of two resistance is 14 and their difference is 6. Determine the two resistances.
- 6. Solution X + y =14....(1) X-y =6 2x=20 x=10
- 7. Substitute x =10 into ..... (1) 10 + y = 14 y=14-10 y=4 The resistance are 10 and 4
- 8. Example 2 X^2 +Y^2= 25 Y= -3X 5 Solution X^2 + y^2 =25..... (1) Y= -3x5...... (2)
- 11. Substitute x=-3x5 Y=-3 (-3)5 Y=4 (0,5) or (-3,4)
- 12. References Larson R, (2014).Precalculus 9th edition, The Pennylvania state University. Cengage Learning.
- 13. Example.