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Solve. 6n + 4 = n – 11 Determine whether each linear relationship is proportional. If so, state the constant of proportionality. Warm Up 116 Write an equation in slopeintercept form for the graph of the linear function. Standards • 8.EE.8 Analyze and solve pairs of simultaneous linear equations. • 8.EE.8b Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple case by inspection. • 8.EE.8c Solve real-world and mathematical problems leading to two linear equations in two variables. To • solve a system of equations by graphing • solve a system of equations by substitution System of Linear Equations A system of linear equations is a set of two or more linear equations containing two or more variables. A solution of a system of linear equations with two variables is an ordered pair that satisfies each equation in the system. Graph and/or Substitute Sometimes it is difficult to identify the exact solution to a system by graphing. In this case, you can use a method called substitution. The goal when using substitution is to reduce the system to one equation that has only one variable. Graph and/or Substitute Not all systems of linear equations have graphs that intersect in one point. There are three possibilities for the graph of a system of two linear equations, and each represents a different solution set. EXAMPLE 1: Solving a System of Equations by Substitution and Graphing Solve the system by substitution and graphing. y = 3x y=x–2 Step 3: Substitute in one of the original equations. Step 1 Write equations as one equation by substituting Step 2 Solve for the variable Ordered Pairs EXAMPLE 2: Solving a System of Equations by Substitution and Graphing Solve the system by substitution and graphing. 2x + 5 = x + 3 –5 2x −x x = −2 -5 =x− 2 −x Substitute in one of the original equations Ordered Pair