Lesson 15 Solving systems of equations by graphing

Lesson 15 Solving systems of equations by graphing

Systems of equations n n n A system of equations is a collection of 2 or more equations containing 2 or more of the same variables. A linear system contains 2 linear equations in 2 like unknowns. Linear systems can be solved by graphing both equations on the same coordinate graph. The point where the 2 lines intersect is the solution.

Solve by graphing n n n 3 y - x = 9 y + x = -1 Put in slope intercept form before graphing y-2 x+4=0 y+x = -1

Using graphing calculator to solve systems n n n 3 x-2 y =6 y+x = 1 put in slope intercept form, so you can enter into calculator To find the exact point of intersection , go to calc 5: intersect, then press enter 3 times until you see intersection.

Classifying systems of equations n n n Solutions are ordered pairs. There are 3 possibilities for the number of solutions to linear system: 1 ordered pair An infinite number of ordered pairs No ordered pairs

n n A linear system that has at least one solution is called consistent. A system with no solution is called inconsistent. A linear system is dependent when one of the equations contains all the solutions common to the other equation in the system. (it would be a multiple of the other equation) Otherwise it is an independent system

Classifying systems n n Consistent consistent inconsistent Independent 1 solution infinite solutions no solution Lines intersect lines coincide lines parallel