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.

1. Solving simultaneous
equations.
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= -3x—5...... (2)

9. Substitute
Y=-3x—5
Into x^2+y^2=25
X=0 or X=-3

10. Y=-3x—5
Y=-3(0)
Y=0—5
Y=-5

11. Substitute x=-3x—5
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.