Lesson 7.1 Solving Linear Systems of Equations by Graphing A ...
Lesson 7.1 Solving Linear Systems of Equations by Graphing A system of linear equations, or linear system, consists of two or more linear equations in the same variables.
A solution of a linear system is an ordered pair that satisfies each equation in the system.
Is the ordered pair
a solution to the linear system?
Now graph the equations.
One way to find the solution of a linear system is by graphing. If the lines intersect in a single point, then the coordinates of the point are the solution of the linear system. Note: the graphing method is very inaccurate, and should therefore always be checked algebraically. Consistent independent system – a linear system with exactly one solution.
Solve the linear system using the graph-and-check method.
Ex. Solving a multi-step problem: Your school is selling football tickets for a home game. The school sold the first day of the sale. Student tickets cost
tickets for
each and non-student tickets costs
on each.
Find the number of student tickets and the number of non-student tickets sold. Write the equations Graph the equations Estimate the point of intersection Check the solution algebraically
A student sells small and large greeting cards decorated at a craft fair. The small cards cost per card, and the large cards cost
per card. The student collects
cards. How many of each type of card did the student sell?
for selling a total of
A solution of a linear system is an ordered pair that satisfies each equation in the system.
Is the ordered pair
a solution to the linear system?
Now graph the equations.
One way to find the solution of a linear system is by graphing. If the lines intersect in a single point, then the coordinates of the point are the solution of the linear system. Note: the graphing method is very inaccurate, and should therefore always be checked algebraically. Consistent independent system – a linear system with exactly one solution.
Solve the linear system using the graph-and-check method.
Ex. Solving a multi-step problem: Your school is selling football tickets for a home game. The school sold the first day of the sale. Student tickets cost
tickets for
each and non-student tickets costs
on each.
Find the number of student tickets and the number of non-student tickets sold. Write the equations Graph the equations Estimate the point of intersection Check the solution algebraically
A student sells small and large greeting cards decorated at a craft fair. The small cards cost per card, and the large cards cost
per card. The student collects
cards. How many of each type of card did the student sell?
for selling a total of
