1. Solving Linear Equation Create by Ching Yun Liu For CI752R

2. Solving Linear Equation Our Objective Understand the relationship between linear equation and graph. Understand every point on the line is a solution for that equation. Introduce linear system with two equations and three possible solutions. Solving linear equations with substitution method. Solving linear equations with addition method.

3. Solving Linear Equations y=2x+4 You can use a graph to present a linear equation. For example, let us draw y=2x+4 Understand the relationship between linear equation and graph. Understand every point on the line is a solution for that equation. Introduce linear system with two equations and three possible solutions. Solving linear equations with substitution method. Solving linear equations with addition method. On the this web site.web site 0 1 2 0 2 3 4 -2 Y=2x+4 (0,4) (-2,0)

4. Solving Linear Equations Let use y = 4x-1 as an example Understand the relationship between linear equation and graph. Understand every point on the line is a solution for that equation. Introduce linear system with two equations and three possible solutions. Solving linear equations with substitution method. Solving linear equations with addition method. Let assume x = -2 then we replace x with -2 y=4*(-2)-1y=(-8)-1y=-9 Therefore -2,-9 is one solution for equation y = 4x-1 ? Question for students Can you find another solution for y=4x-1 There are some solutions for y=4x-1 {(x,y)|(-1,-5), (0,-1), (1,3), (2,7)}

5. Solving Linear Equations Understand the relationship between linear equation and graph. Understand every point on the line is a solution for that equation. Introduce linear system with two equations and three possible solutions. Solving linear equations with substitution method. Solving linear equations with addition method. Let us put {(x,y)|(-1,-5), (0,-1), (1,3)} on the graph (-1,-5) (0,-1) (1,3) Y=4x-1

6. Solving Linear Equations Understand the relationship between linear equation and graph. Understand every point on the line is a solution for that equation. Introduce linear system with two equations and three possible solutions. Solving linear equations with substitution method. Solving linear equations with addition method. Two lines across at one point, which means that two equations have only one solution For example x+y=0, x-2y=1 Two lines are parallel, which means that two equations have no solution For example 2x-3y=0, 2x-3y=2 Two lines are overlap, which means that two equations have unlimited solution For example x+3y=1, 2x+6y=2 0 0 x+y=0 X-2y=1 0 0 2x-3y=0 2x-3y=2 0 0 X+3y=1 2x+6y=2

7. Solving Linear Equations 1.Solve one equation for a variable, say y. 2.Substitute the expression obtained for y for all occurrences of y in the other equation. 3.Solve the resulting equation. 4.Substitute the solution found in the Step 3 in the equation found in Step 1 and solve for y. Understand the relationship between linear equation and graph. Understand every point on the line is a solution for that equation. Introduce linear system with two equations and three possible solutions. Solving linear equations with substitution method. Solving linear equations with addition method. Let us use 3x+y=1, -x+2y=9 as an example 1.Solve one equation for a variable, say y. 3x+y=1 change to y=1-3x 2.Substitute the expression obtained for y for all occurrences of y in the other equation. -x+2y=9 become –x+2(1-3x)=9 3.Solve the resulting equation. –x+2(1-3x)=9 -x+(2-6x)=9  -x+2-6x=9  –x-6x=9-2 -x+(2-6x)=9  -x+2-6x=9  –x-6x=9-2  -7x=7 -x=1  x=-1  -7x=7  -x=1  x=-1 4.Substitute the solution found in the Step 3 in the equation found in Step 1 and solve for y. 3x+y=1 replace x with –1 then 3(-1)+y=1 -3+y=1 y=1+3=4 -3+y=1 y=1+3=4 The solution for 3x+y=1, -x+2y=9 is (-1,4) The solution for 3x+y=1, -x+2y=9 is (-1,4)

8. Solving Linear Equation Understand the relationship between linear equation and graph. Understand every point on the line is a solution for that equation. Introduce linear system with two equations and three possible solutions. Solving linear equations with substitution method. Solving linear equations with addition method. 3x+y=1, -x+2y=9 Now lets plot this two equations 3x+y=1, -x+2y=9 to check our solution. 0 0 3x+y=1 -x+2y=9 (-1,4)

9. Solving Linear Equations 1.The positions of any two equations of the system can be interchanged. 2.Both sides of any equation of the system can be multiplied of divided by the nonzero constant. 3.Any equation of the system can be altered by adding to its sides a constant multiple of the corresponding sides of another equation of the system. Understand the relationship between linear equation and graph. Understand every point on the line is a solution for that equation. Introduce linear system with two equations and three possible solutions. Solving linear equations with substitution method. Solving linear equations with addition method. Let us use 3x+y=1, x-2y=-9 as an example 1.The positions of any two equations of the system can be interchanged. x-2y=-9  -x+2y=9 x-2y=-9  -x+2y=9 2.Both sides of any equation of the system can be multiplied of divided by the nonzero constant. -x+2y=9  3(-x+2y)=3*9  -3x+6y=27 -x+2y=9  3(-x+2y)=3*9  -3x+6y=27 3.Any equation of the system can be altered by adding to its sides a constant multiple of the corresponding sides of another equation of the system. x-2y=-9-3x+6y=27 Are x-2y=-9 and -3x+6y=27 same equations? 3x + y= 1 + -3x+6y=27 + -3x+6y=27 = 0+7y=28  y=4 = 0+7y=28  y=4 So x-2*4=-9  x-8=-9  x=-1 The solution for 3x+y=1, x-2y=-9 is (-1,4)

10. Solving Linear Equation Understand the relationship between linear equation and graph. Understand every point on the line is a solution for that equation. Introduce linear system with two equations and three possible solutions. Solving linear equations with substitution method. Solving linear equations with addition method. 3x+y=1, x-2y=-9 Now lets plot this two equations 3x+y=1, x-2y=-9 to check our solution. 0 0 3x+y=1 X-2y=-9 (-1,4)