LInear Systems Word Problems

A linear system is a collection of two or more linear equations involving the same variables.

To solve a linear system means to find the values of the variables that satisfy all equations in the system simultaneously.

The graphical representation of a linear equation is a straight line on a coordinate plane.

1. One solution (the lines intersect at one point). 2. No solution (the lines are parallel). 3. Infinitely many solutions (the lines coincide).

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Identify the variables, translate the relationships and conditions into equations, and ensure they reflect the problem's constraints.

A coefficient is a numerical factor that multiplies a variable in an equation.

Two equations are equivalent if they have the same solution set.

Substitute the values of the variables back into the original equations to verify that they satisfy all equations.