Happy Summer Birthday to: Dylan Hare

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Presentation transcript:

Happy Summer Birthday to: Dylan Hare October 13th Happy Summer Birthday to: Dylan Hare

Solving Linear Systems by Elimination: Step One: Make sure the equations are aligned. They have to be in standard form. Step Two: Add/subtract the equations to eliminate one variable. Step Three: Solve for the left over variable. Step Four: Substitute the value into either original equation to solve for the other variable. Answer: An ordered pair (x, y).

Solving Linear Systems by Elimination: Solve the linear system by elimination (adding or subtracting). Check your solution. 1) 3x + 4y = 8 -3x + 5y = 10

Solving Linear Systems by Elimination: Solve the linear system by elimination. Check your solution. 2) 2x + 3y = 11 -2x + 5y = 13

Solving Linear Systems by Elimination: Addition & Subtraction Solve the linear system by elimination. Check your solution. 3) 5x + 6y = 4 7x + 6y = 8

Solving Linear Systems by Elimination: Addition & Subtraction Solve the linear system by elimination. Check your solution. 4) 4x + 3y = 2 5x + 3y = -2

Solving Linear Systems by Elimination: Addition & Subtraction Solve the linear system by elimination. Check your solution. 5) 9x – 3y = 18 3y = -7x + 30

Solving Linear Systems by Elimination: Addition & Subtraction Solve the linear system by elimination. Check your solution. 6) 8x – 4y = -4 4y = 3x + 14

Solving Linear Systems by Elimination: Multiplication Solve the linear system by elimination . Check your solution. 7) 3x – 3y = 21 8x + 6y = -14

Solving Linear Systems by Elimination: Multiplication Solve the linear system by elimination (adding or subtracting). Check your solution. 8) 6x + 5y = 19 2x + 3y = 5

Special Types of Linear Systems Sometimes when we are solving linear systems, strange things can happen, and it seems like we’ve made a mistake. These things happen when the two lines are parallel or when they are the exact same line. It’s obvious when we graph it, but let’s talk about what happens when we try to solve a “strange problem” like this by elimination or substitution.

Special Types of Linear Systems Solve the linear system by elimination. Check your solution by graphing both lines in the calculator. 9) 2x + 4y = 6 x + 2y = 3

Special Types of Linear Systems Solve the linear system by elimination. Check your solution by graphing both lines in the calculator. 10) y = 2x – 3 y = 2x + 3

Special Types of Linear Systems So in summary: a false statement such as 1 = 8, means the lines are parallel. “no solution” a true statement, such as 2 = 2, means the lines are the same line. “infinitely many solutions”

11) Yummy bakery sells apple and blueberry pies each Saturday 11) Yummy bakery sells apple and blueberry pies each Saturday. Apple pies cost $8 each and blueberry pies cost $12 each. Last Saturday, the bakery sold 4 more apple pies than blueberry pies for total sales of $232. Which system of equations can be used to find a, the number of apple pies and b, the number of blueberry pies sold? A. 8a + 12b = 232 B. 8a + 12b = 232 b = a + 4 a = b + 4 C. 8a + 12b = 232 D. 8a + 12b = 232 a + b = 4 a = b – 4

12) Tom has 3 more dimes than quarters. Together he has $2. 75 12) Tom has 3 more dimes than quarters. Together he has $2.75. How many of each type of coin does he have?

Homework WS