3.1 Intro to Systems
 You are solving for the variable that makes theequation true (equal).When you solve one variable equations2x - 4 = 6 You are solving for the variable that makes theequation true (equal).When you solve one variable equations2x - 4 = 6+4+4Add 4 to both sides You are solving for the variable that makes theequation true (equal).When you solve one variable equations2x - 4 = 62x = 10+4+4Fill in the correct value You are solving for the variable that makes theequation true (equal).When you solve one variable equations2x - 4 = 62x = 10+42+42 You are solving for the variable that makes theequation true (equal).When you solve one variable equations2x - 4 = 62x = 10+42x = 5+42 You are solving for the variable that makes theequation true (equal).When you solve one variable equations2x - 4 = 62x = 10+42x = 5+42 You are solving for the number that can go in for xWhen you solve one variable equations2x - 4 = 62x - 4 = 62x = 102x = 5x = 5+42+42( 5 ) -4 = 6Plug in 5 for xin the originalequation to check There are many sets of possible solutionsFor a two variable equations x + y = 5such as: x = 1There are many sets of possible solutionsy = 4For a two variable equationsFor a two variable equations because 1 + 4 = 5x + y = 5such as: x =2x = 1Fill in the correct valueThere are many sets of possible solutionsy = 3y = 4For a two variable equationsFor a two variable equations because 2 + 3 = 5because 1 + 4 = 5x + y = 5such as: x =2x = 100x = 1There are many sets of possible solutionsy = 3y = 4y = -95For a two variable equationsFor a two variable equations because 2 + 3 = 5because 1 + 4 = 5because 100 - 95 = 5x + y = 5Fill in the correct valuesuch as: x =2x = 100x = 1In fact, the number of solutions are infiniteThere are many sets of possible solutionsy = 3y = 4y = -95For a two variable equationsFor a two variable equations because 2 + 3 = 5because 1 + 4 = 5because 100 - 95 = 5x + y = 5such as: But if I have two equationseach with two variablesx + y = 5x - y = -3 I can solve for the x and y values that work for BOTHThe x and y values that make both equations trueBut if I have two equationseach with two variablesx + y = 5x - y = -3 I can solve for the x and y values that work for BOTHSolutionsPossibleBut if I have two equationseach with two variablesx + y = 5x - y = -3 I can solve for the x and y values that work for BOTHx = 0  y = 5SolutionsPossibleBut if I have two equationseach with two variablesx + y = 5x - y = -3 x = 1  y = 4I can solve for the x and y values that work for BOTHx = 0  y = 5SolutionsFill in the correct valuePossibleBut if I have two equationseach with two variablesx + y = 5x - y = -3 x = 2  y = 3x = 1  y = 4I can solve for the x and y values that work for BOTHx = 0  y = 5SolutionsPossibleFill in the correct valueBut if I have two equationseach with two variablesx + y = 5x - y = -3 x = 2  y = 3x = 1  y = 4I can solve for the x and y values that work for BOTHx = 0  y = 5SolutionsPossibleBut if I have two equationseach with two variablesx + y = 5x - y = -3SolutionsPossible x = 2  y = 3x = 1  y = 4I can solve for the x and y values that work for BOTHx = 0  y = 5SolutionsPossibleBut if I have two equationseach with two variablesx + y = 5x - y = -3x = 0  y = 3SolutionsPossible x = 2  y = 3x = 1  y = 4I can solve for the x and y values that work for BOTHx = 0  y = 5SolutionsPossibleBut if I have two equationseach with two variablesx + y = 5x - y = -3x = 0  y = 3x = 1  y = 4SolutionsPossible x = 2  y = 3x = 1  y = 4I can solve for the x and y values that work for BOTHx = 0  y = 5SolutionsPossibleBut if I have two equationsDrag in the valueseach with two variablesx + y = 5x - y = -3x =     y =  x = 0  y = 3x = 1  y = 4SolutionsPossible2?5? x = 2  y = 3x = 1  y = 4I can solve for the x and y values that work for BOTHx = 0  y = 5SolutionsPossibleBut if I have two equationsThe set that matcheseach with two variablesis the answerx + y = 5x - y = -3x = 2  y = 5x = 0  y = 3x = 1  y = 4SolutionsPossible x = 2  y = 3x = 1  y = 4I can solve for the x and y values that work for BOTHx = 0  y = 5SolutionsPossibleBut if I have two equationsThe set that MATCHESeach with two variablesis the answerx + y = 5x - y = -3x = 2  y = 5x = 0  y = 3x = 1  y = 4SolutionsPossible When x=1 and y=4 which equation(s) are true (equal)?2nd equation1st equationx = 1 and y = 4 is the solution to this system1st equation only2nd equation onlyNeither equation Both equationsx + y = 5x - y = -3 Substitute x=4, y=1 (4,1) into both equationsto see if (4,1) is a solution of the system of equations.2nd equation1st equationWhen x=4 and y=1which equation(s)are true?2x - y =  4x + y = 51st equation only2nd equation onlyNeither equation Both equations Substitute x=4, y=1 (4,1) into both equationsto see if (4,1) is a solution of the system of equations.2nd equation1st equationWhen x=4 and y=1which equation(s)are true?2x - y =  4x + y = 5Point (4,1) onlySat-is-fiesthe 1st equation.(4,1) is NOT a solutionto the entire system Substitute x=2, y=0 (2,0) into both equationsto see if (2,0) is a solution of the system of equations.2nd equation1st equationWhen x=2 and y=0which equation(s)are true?2x - y =  4x + y = 51st equation only2nd equation onlyNeither equation Both equations Substitute x=2, y=0 (2,0) into both equationsto see if (2,0) is a solution of the system of equations.2nd equation1st equationWhen x=2 and y=0which equation(s)are true?2x - y =  4x + y = 5Point (2,0) onlySat-is-fiesthe 2nd equation.(2,0) is NOT a solutionto the entire system Substitute x=3, y=2 (3,2) into both equationsto see if (3,2) is a solution of the system of equations.2nd equation1st equationWhen x=3 and y=2which equation(s)are true?2x - y =  4x + y = 51st equation only2nd equation onlyNeither equation Both equations Substitute x=3, y=2 (3,2) into both equationsto see if (3,2) is a solution of the system of equations.2nd equation1st equationWhen x=3 and y=2which equation(s)are true?2x - y =  4x + y = 5Both equations are true.(3,2) is a solution of thissystem of equations The End
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