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Sstems of Linear Equations bjectives: SLVE SYSTEMS BY GRAPHING 1 After this lesson I will be able to solve a sstem of equation b graphing. 2 After this lesson I will be able to identif the number of solutions a sstem So what is a of equation has, b graphing. sstem and wh is it messing with our linear equations? A sstem is when man things work together. We see eamples of sstems ALL THE TIME in science class! The WATER CYCLE is a sstem because everthing has to work together! A sstem of linear equations is when two lines work together or touch when graphed on the same coordinate plane. + = If the do touch, the point ( s ) at which the touch are the solution ( s ) : (, )

EXPLRE: How man was can straight lines cross? TR using our arms: Your left arm as one LINEAR EQUATIN, and the right arm as the other LINEAR EQUATIN. How man was can ou get them to cross? SCENARI 1: Well, we know we can DEFINITELY have our arms NEVER touching! If we graph two lines on the same coordinate plane and the do not cross, we sa the sstem consists of two parallel lines and has N solutions. No Solutions SCENARI 2: We also BVIUSLY know that we can have our arms cross onl at one point! If we graph two lines on the same coordinate plane and the cross at one points, we sa that point (,) is the solution to the sstem of linear equations. ne Solution SCENARI 3: But did ou think of the scenario where our arms would be ling on top of one another? This is when a sstem has an infinite amount of solutions. HINT - it means the lines are the same. Infinite Solutions

Sstems of Linear Equations g r a p h i n g Keep in mind, SYSTEMS F LINEAR EQUATINS allow for us to evaluate two linear equations at the same time!!! Remember how we found out how man solutions a sstem had b using our arms? NNE NE INFINITE PRACTICE: Use the graph to the right to determine whether the sstem of linear equations has NNE, NE, or INFINITE solutions. 1 = - - 3 2 = - 1 2 + 2 = -6 = - - 3 2 + 2 = 4 3 + = 3 2 + 2 = -6 3 = - - 3 4 2 + 2 = -6 = - 1 2 + 2 = 4 3 + = 3 = - - 3

eems to lie on both lines. Check this estimate with 3 and with 1 in each equation. 1 or 4 (3, 1). Sometimes the will make us graph our own ( 3, 1) linear equations to discover how man solutions the sstem has. = -2 + 1 = 3-1 ncide. Therefore there are infinitel s. 7 = 1 / 2 + 0 8 = - 2 / 3-1 tem of equations. Then determine whether the sstem has no lution, or infinitel man solutions. If the sstem has one solution, = -2 + 6 = 2 + 2 1 2 2. 2 3. 2 1 3 9 5. 3 = 2 / 3 2 + 3 6 6. 2 4 = -2 + 42 3 2 4 2 2 = 2 / 3-2 10 = -2 + 2 P R A C T I C E 56 = -2-1 = -2 + 2 4 2 1 2 4 2 7 Glencoe Algebra 1

Practice on our own: Graphing Sstems of Linear Equations Use the graph below to determine whether the sstem of linear equations has NNE, NE, or INFINITE solutions. 1 = - + 2 2 = + 1 = - + 2 3 + 3 = -3 = - + 2 = - - 1 = + 1 3 3 + 3 = -3 = - - 1 3 + 3 = -3 Graph the sstems below, stating how man solutions the sstem has: 4 = 3-4 = -3 + 2 5 = 1 / 3 + 3 = - 2 / 3-3 6 = 5 / 4-2 = 5 / 4-1

Sstems of Linear Equations bjectives: SLVE SYSTEMS BY GRAPHING 1 After this lesson I will be able to solve a sstem of equation b graphing. 2 After this lesson I will be able to identif the number of solutions a sstem So what is a of equation has, b graphing. sstem and wh is it messing with our linear equations? A sstem is when man things work together. EVAPRATIN PERCIPITATIN We see eamples of sstems ALL THE TIME in science class! CNDENSATIN The PERCIPITATIN WATER CYCLE is a sstem because everthing has to work EVAPRATIN CLLECTIN together! A sstem of linear equations is when two lines work together or touch when graphed on the same coordinate plane. + = If the do touch, the point ( s ) at which the touch are the solution ( s ) : (, )

Sstems of Linear Equations g r a p h i n g Keep in mind, SYSTEMS F LINEAR EQUATINS allow for us to evaluate two linear equations at the same time!!! Remember how we found out how man solutions a sstem had b using our arms? NNE NE INFINITE PRACTICE: Use the graph to the right to determine whether the sstem of linear equations has NNE, NE, or INFINITE solutions. 1 = - - 3 2 = - 1 2 + 2 = -6 = - - 3 2 + 2 = 4 3 + = 3 NE INFINITE 2 + 2 = -6 3 = - - 3 4 2 + 2 = -6 = - 1 2 + 2 = 4 3 + = 3 NNE NE = - - 3

eems to lie on both lines. Check this estimate with 3 and with 1 in each equation. 1 or 4 (3, 1). Sometimes the will make us graph our own ( 3, 1) linear equations to discover how man solutions the sstem has. = -2 + 1 = 3-1 ncide. Therefore there are infinitel s. 7 = 1 / 2 + 0 8 = - 2 / 3-1 NE NNE tem of equations. Then determine whether the sstem has no lution, or infinitel man solutions. If the sstem has one solution, = -2 + 6 = 2 + 2 1 2 2. 2 3. 2 1 3 9 5. 3 = 2 / 3 2 + 3 6 6. 2 4 = -2 + 42 3 2 4 2 2 = 2 / 3-2 NE 10 = -2 + 2 P R A C T I C E 56 = -2-1 = -2 + 2 4 2 1 2 4 2 NE NNE INFINITE 7 Glencoe Algebra 1

Practice on our own: Graphing Sstems of Linear Equations NAME: Use the graph below to determine whether the sstem of linear equations has NNE, NE, or INFINITE solutions. 1 = - + 2 2 = + 1 NE = - + 2 3 + 3 = -3 NNE = - + 2 = - - 1 = + 1 3 3 + 3 = -3 = - - 1 INFINITE 3 + 3 = -3 Graph the sstems below, stating how man solutions the sstem has: 4 = 3-4 = -3 + 2 5 = 1 / 3 + 3 = - 2 / 3-3 6 = 5 / 4-2 = 5 / 4-1 NE NE NNE