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When solving systems of equations, you have three types of possible solutions. Solutions to Systems of Equations One Solution.... This is when you are able to solve the equations to find the value of each variable. (x,y) One solution.... In a graph In substitution Point of intersection is (2 , 7) so the system has ONE solution.... You are able to use substitution to find the value of both variables ie: x = 2 & y = 7 (2,7) No Solutions.... When solving, the variables are canceled out leaving two DIFFERENT numbers. This is when you are unable to solve the equations to find the value of each variable. Parallel lines No point of intersection. No solution.... In a graph In substitution so the system has NO solution.... When using substitution, you are unable to find the value of the variables...they cancel outto leave two DIFFERENT numbers... ie: 2 = 7 ....an untrue statement Infinitely Many Solutions.. When solving, the variables are canceled out leaving the SAME numbers. This is when you are unable to solve the equations to find the value of each variable. Infinitely Many Solutions.. The SAME LineNo point of intersection. so In a graph In substitution the system has INFINITELY MANY solutions... When using substitution, you are unable to find the value of the variables...they cancel outto leave the SAME numbers... ie: 7 = 7 ....an true statement What is the solution to the following system of equations? Solve by graphing. y = 3x + 6y = - x + 2 (-1,3) No Solution Infinitely Many Solutions What is the solution to the following system of equations? Solve by graphing. y = 4x + 4y = 4x + -1 Infinitely Many Solutions (-1,4) No Solution What is the solution to the following system of equations? No Solution Infinitely Many Solutions (-1,-2) Solve by substituting. y = 2x - 16x - 2y = 2 What is the solution to the following system of equations? No Solution Infinitely Many Solutions (4,3) Solve by substituting. 2x - 5 = y-1 + x = y What is the solution to the following system of equations? (4,10) No Solution Infinitely Many Solutions Solve by substituting. y = 2x - 24x - 2y = 10 Let's Review.... When a system of equations has infinitely many solutions, the solution looks like and the graphed lines are . When a system of equations has no solution, the solution looks like and the graphed lines are . When a system of equations has one solution, the solution looks like and the graphed lines . use the numbers 3 and 8 to answer the following questions and DO NOT skip spaces After completing this review,what is your level of understanding? Rating Scale: 4 - I understand it and can teach it 3 - I understand it 2 - I can do it with more practice/the use of my notes 1 - I still don't understand |