1. Midterm Notes ABI101

2. Simultaneous Equations Simultaneous Equations are a set of equations containing multiple variables.equations This set is often referred to as a system of equations. A solution to a system of equations is a particular specification of the values of all variables that simultaneously satisfies all of the equations. To find a solution, the solver needs to use the provided equations to find the exact value of each variable. Methods to solve simultaneous equations: graphical method matrix method matrix substitution method elimination or addition method

3. Examples of Simultaneous Equations 2x + y = 8, x + y = 6 x – y = 10, 2y + 7 = 1 ½ x + 3y = 2, 3x + y = 0

4. Examples of NON Simultaneous Equations 2x + 2y = 4, x + y = 2 ½ y + 2x = 3, y + 4x = 6 X – y = 3, 3x – 3y = 9 What is about these??? X – y = 3, 3x + 3y = 9 2x + 3y = 6, 3x + 4y = 7

5. Solution for Simultaneous Equations Example X + y = 2, 2x – 2y = 0 X + y = 2...... 2x – 2y = 0 …… X + y = 2  x = 2 – y from Substitute in : 2(2 - y) – 2y = 0 4 – 2y – 2y = 0  4 – 4y = 0  4 = 4y  y = 4/4 =1 x = 2 – 1 = 1 1 2 1 2

6. The Graphical Method The graphical solution of linear simultaneous equations is the point of intersection found by drawing the two linear equations on the same axes. Example 1 Solve the following simultaneous equations graphically.

7. The Graphical Method Solution: The graphical solution of the simultaneous equations is given by the point of intersection of the linear equations. Consider x + y = 8. x-intercept: When y = 0, x = 8 y-intercept: When x = 0, y = 8 Consider x – y = 2. x-intercept: When y = 0, x = 2 y-intercept: When x = 0, -y = 2  y=-2

8. The Graphical Method