1. Chapter 7.3

2.  Objective NCSCOS 4.03  Students will know how to solve a system of equations using addition

3.  What is a system of equations?  Two equations where we try and find their intersection.

4.  What are the possible solutions to a system of equations? One solution – an ordered pair where the two lines intersect No solution – the lines are parallel so they have no points of intersection Infinitely many solutions – they are the same line so every point on one line is the same as the other line

5.  Example 1: Use addition to solve the system of equations:

6.  To solve a system of equations we have to eliminate one of the variables  If we were to add these together could we eliminate one of the variables?  Yes, the y’s add up to zero!  We can add the equations together to “get rid” of the y’s

7.  We add the equations  x + 3x = 4x  -3y + 3y = 0  We don’t write 0y so it goes away  7 + 9 = 16

8.  Solve for x  Divide both sides by 4  4 is the x value in the point where the two lines intersect

9.  Once you know x, plug it into either equation to find the y value  We’ll use the first one

10.  Substitute 4 for x  Subtract 4 from both sides  Divide by -3  -1 is the y value for the point where the 2 lines intersect

11.  Example 1: Use addition to solve the system of equations:  The solution to this problem is the point where they intersect  The answer is:

12.  Solve the following system of equations 1. x – 2y = 4 2x + 2y = 2 3. 2x – 5y = -4 4x + 5y = -8 5. -6x + 4y = -10 2x – 4y = -2 4. -3x – 2y = 4 2x + 2y = -2 2. x + 4y = 3 3x – 4y = -7

13.  Solve the following system of equations 1. x – 2y = 4 2x + 2y = 2 3. 2x – 5y = -4 4x + 5y = -8 5. -6x + 4y = -10 2x – 4y = -2 4. -3x – 2y = 4 2x + 2y = -2 2. x + 4y = 3 3x – 4y = -7 1.(2, -1) 2. (-1, 1) 3. (-2, 0) 4. (-2, 1) 5. (3, 2)

14.  Example 2: Solve the following system of equations:  Does it matter which variable I solve for first? No!

15.  This problem we will have to solve for y first since the x’s add up to zero  Add the two equations  Divide by 3

16.  Plug the y value into either equation  Solve for x

17.  Solve the following system of equations: 1. -x + 3y = 7 x + y = -1 3. -4x + 2y = 2 4x – 2y = 4 4. 3x + 2y = 9 -3x – 8y = 3 5. -2x + 3y = -2 2x – 6y = -4 2. -2x + 3y = 7 2x – 4y = -3

18.  Solve the following system of equations: 1. -x + 3y = 9 x + y = -1 3. -4x + 2y = 2 4x – 2y = 4 4. 3x + 2y = 8 -3x – 8y = 4 5. -2x + 3y = -2 2x – 6y = -4 2. -2x + 3y = 8 2x – 4y = -4 1.(-3, 2) 2.(-10, -4) 3.No Solution 4.(4, -2) 5.(4, 2)