CA Standard Algebra I 9.0 True Collaboration means that the final product is impossible without the contributions of all collaborators. Discourse on Systems of Equations

WARMING up to Linear Systems Solved by Substitution Change the following linear equation from Standard Form: (Ax + By = C) to Slope Intercept Form: y = mx + b Solve for “y”: 1. 2x + y = 4 y = -2x x What was the operation that changed this equation?

Getting Warmer…Standard Form to Slope-Intercept Form Solve for “y” 2. -3x + y = x + 2y = 8 3. x + y = 7 -2x 2y = -2x y = -x + 4

Hot Stuff: Solve for “y” x + 4y = x - 10y = x - y = x -3x -y = -3x y = 3x + 11

Solve the system of Linear Equations Standard Form -2x + y = 15 +2x +2x y = 2x + 15 Remember: y = y, so… -4x + y = 7 +4x +4x y = 4x + 7 2x + 15 = 4x x -2x 15 = 2x = 2x 4 = x

We Know THE SOLUTION TO A SYSTEM OF EQUATIONS IS AN ORDERED PAIR (x, y) where the x and y values satisfy each equation of the system For the system: -2x + y = 15 -4x + y = 7 We solved for x = 4 So, we have part of the solution: (4, y) How do we solve for y? Does it matter which equation we substitute the x value? Let’s try both…. Compare your answer with your partner. Show me your answer on your white board.

Solve the system of Linear Equations Standard Form -4x + 2y = x +4x 2y = 4x y = 2x - 6 Remember: y = y, so… 9x + 3y = 27 -9x -9x 3y = -9x y = - 3x + 9 2x – 6 = -3x x +3x 5x - 6 = x = 15 x = 3

We Know THE SOLUTION TO A SYSTEM OF EQUATIONS IS AN ORDERED PAIR (x, y) where the x and y values satisfy each equation of the system For the system: -4x + 2y = -12 9x + 3y = 27 We solved for x = 3 So, we have part of the solution: (3, y) How do we solve for y? Does it matter which equation we substitute the x value? Let’s try both…. Compare your answer with your partner. Show me your answer on your white board.

Collaboration: To solve the system, you will share the problem and teach your part to your partner Student Left Student Right Transform the first equation from Standard to Slope-Intercept Form Tell your partner what step(s) you took Write the equations down as a y = y statement Continue taking turns with the steps Transfer your given equation from Standard to Slope-Intercept Form Tell your partner what step(s) you took. Do the first step to solve the substitution problem for “x” Last step is to substitute for y, then write the solution

Graph to Check your Solution GRAPH EACH EQUATION ON THE SAME COORDINATE PLANE. What is the connection between the point where the lines intersect and the algebraic solution of the Linear System? ( 2, 12) -3x + y = 6 4x + y = 20 y = 3x + 6 y = -4x + 20 ( 2, 12)

Student Choice For Problem Number Four you can continue to work with your partner and share the work, or each of you can solve it and compare your answers. When you have finished #4, check in with your teacher, then complete the survey on the last page of your packet Talk to your partner about the answers to the survey. Turn in only one completed survey for each group of students

YOU ARE A STAR I KNEW YOU COULD DO IT