Chapter 8 Systems of Equations 8.1 Solve Systems by Graphing 8.2 Solve Systems by Substitution 8.3 Solve Systems by Addition 8.4 Using Systems to Solve Word Problems 8.5 Motion Problems 8.6 Digit and Coin Problems

8.1 Solving Systems of Equations by Graphing Objectives: To determine the whether an ordered pair is a solution of a system To find the solution by graphing each equation

Systems of Equations A pair of equations with two variables A solution is an ordered pair (x,y) that makes BOTH equations true. We can approximate the solution by graphing; the solution is that point where the lines intersect.

Determine whether (1,2) is a solution of : y = x + 1 and 2x + y = 4 1 + 1 2(1)+ 2 4 2 4 (1,2) is a solution of the system.

Determine whether (-3,2) is a solution of : a + b = -1 and b + 3a = 4 -3 + 2 -1 4 2 + 3(-3) 2 - 9 (-3,2) is not a solution of the system.

Review Graphing Linear Equations Table X and Y –intercepts Slope intercept form (y=mx+b)

When we graph a system of two linear equations, one of three things may happen: The lines have one point of intersection. This point is the only solution of the system. (consistent) The lines are parallel. If this is so, there is no point that satisfies both equations. There is no solution (inconsistent) The lines coincide. Thus the equations have the same graph and there is an infinite number of solutions. (dependent)

Solve by graphing: x + 2y = 7 and x = y + 4 (5,1) is the solution

Solve by graphing: 3y - 2x = 6 and 2x – 3y = 12 no solution

Solve by graphing: 3y - 2x = 6 and 2x – 3y = 6 Many solutions

Solve by graphing: x + 4y = -6 and 2x – 3y = 10 (2,-2)

Solve by graphing: y = 2x + 1 and 2y + 4x = 10 (1,3)

Assignment Page 360 2 – 20 even and 21,22,23 Use graph paper