Solving Systems of Equations by Graphing

Table of Contents 46: Warm-Up 47: How Do I Solve a System of Equations by Graphing?

Warm Up Graph the following equations on the same coordinate grid. Graph each equation in a different color. 1. f(x) = 4x – 1 2. g(x) = ½x + 1 3. h(x) = -x 4. x = 6 5. y = -3

Warm-Up 1. f(x) = 4x – 1 2. g(x) = ½x + 1 3. h(x) = -x 4. x = 6 5. y = -3

Learning Intention/Success Criteria LI: We are learning how to solve a system of equations by graphing SC: I know how to -determine if a system of equations has many, none, or one solution(s) -solve systems of two linear equations in two unknowns by graphing -read solutions to system of equations off the graph of two functions -graph a linear equation

EQ: How Do I Solve a System of Equations by Graphing? 5/5/2019

System of Equations A set of two or more equations that contain two or more variables, including nonlinear equations Solution to a System The ordered pair(s) that satisfy all equations in the system at the same time Called the point of intersection 3 solution types: no solution, many solutions, one solution

One Solution The two lines cross each other in exactly one spot on the graph There will be an answer for x and y Solution written: (x, y)

Infinite Solutions Two lines are graphed on top of each other Both sides of the equation will equal the same thing No Solution The two lines never cross each other The two sides of the equations will not equal each other

Fold both papers with the white paper on the inside

Staple Staple Staple 1. Staple the whole packet three times near the fold 2. Cut only the top two layers, creating three spaces in total

Staple Staple Staple One Solution x = a

Staple Staple

Solve by graphing: { y = -1/3x + 3 y = 2x - 4 Solution: (3, 2)

{ Guided Practice 1 Find the solution to the given system by graphing: y = 2x - 5 y = -3x + 2 2 Solution: (2, -1)

Staple Staple Staple No Solution a = b One Solution x = a

Staple Staple Staple One Solution x = a

Solve by graphing: { y = -4/3x + 5 y = -4/3x Solution: No Solution

{ Guided Practice 2 Find the solution to the given system by graphing: y = 2x + 4 y = 6x 3 Solution: No Solution

Staple Staple Staple No Solution a = b Many Solutions a = a One Solution x = a

Staple Staple Staple No Solution a = b One Solution x = a

Solve by graphing: { y = 3x - 1 y = 3x - 1 Solution: Many Solutions

{ Guided Practice 3 Find the solution to the given system by graphing: y = -2x - 1 y = -4x – 1 2 Solution: Many Solutions