EDGE Math 8

Solutions to Systems of Two Linear Equations in Two Variables

A set of equations such as

{\begin{array}{l} x + 2 y = 7 \\ - x + y = 2 \end{array}

is called a system of equations. Each equation is a linear equation in two variables since it is of the form $A x + B y = C,$ where A, B, and C are constants, and A and B are both not equal to zero. As such, the pair of equations is called a system of linear equations in two variables.

Example

Translate the problem situation below into a system of equations. Do not solve.

At a city terminal, the number of wheels of jeepneys and tricycles add up to 25. Is it possible for the total number of wheels of all the jeepneys and tricycles to be 71?

Solution

Let x = number of wheels of jeepneys and number of wheels of tricycles. Since the total number of wheels of jeepneys and tricycles is 25,

x + y = 25.

Furthermore, the total number of wheels of both types of vehicles is 71. Hence,

4 x + 3 y = 71.

The problem yields a system of two linear equations in two variables.

{\begin{array}{l} x + y = 25 \\ 4 x + 3 y = 71 \end{array}