Linear Systems
· A linear system is a set of two or more lines that intersect each other. This point of intersection is the solution to a linear system.
· There are two methods to solve a linear system.
o Method of substitution
§ Write all equations in y = mx + b form.
§ Number the equations 1 and 2.
§ Substitute the equations into each other. mx + b = mx + b
§ Solve for x.
§ Substitute x into any one of the original equations.
§ Solve for y.
§ Place x and y as a co-ordinate.
o Method of elimination
§ Number the equations 1 and 2.
§ Multiply one or both equations to have the same co-efficient for the same variable. The sign of the co-efficient isn't considered.
§ Subtract or add the equations to make the value of one variable 0.
§ Solve for the other variable.
§ Substitute the value of one variable into any one of the original equations.
§ Solve for the remaining variable.
§ Place x and y as a co-ordinate.
· There are two methods to solve a linear system.
o Method of substitution
§ Write all equations in y = mx + b form.
§ Number the equations 1 and 2.
§ Substitute the equations into each other. mx + b = mx + b
§ Solve for x.
§ Substitute x into any one of the original equations.
§ Solve for y.
§ Place x and y as a co-ordinate.
o Method of elimination
§ Number the equations 1 and 2.
§ Multiply one or both equations to have the same co-efficient for the same variable. The sign of the co-efficient isn't considered.
§ Subtract or add the equations to make the value of one variable 0.
§ Solve for the other variable.
§ Substitute the value of one variable into any one of the original equations.
§ Solve for the remaining variable.
§ Place x and y as a co-ordinate.