Learning Outcomes earning Outcomes • To solve simultaneous linear equations in two unknowns.
• To solve simultaneous equations involving linear equations and equations of order two in two unknowns.
• To model and solve word problems involving simultaneous equations.
Systems of Sim ultaneous Equations 7 Systems of simultaneous equations
A system of simultaneous equations consists of two or more equations in two or more unknowns.
2x + 3y = 7 3x − 5y = 1
This set of two equations has two unknowns, x and y. The solution of this system of simultaneous equations is the values of x and y that make both equations true at the same time (simultaneously). There are two different types to be considered.
7.1 Linear equations in two unknowns Y 8
ACTIVITY
ACTION Working with simultaneous equations
OBJECTIVE To learn the techniques needed to solve linear simultaneous equations
These are simultaneous equations of the form: ax + by = d ex + f y = g
1. The unknowns are x and y in this case.
2. The coeffi cients of x and y are a, e and b, f , respectively. The constants are d and g.
3. They are called linear equations because if you plot y against x for each equation, you get a straight line.
The method of solution is called elimination by addition.
