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3.3.2 – Types of Solutions

3.3.2 – Types of Solutions. Using elimination or substitution, we have found 2 ways to solve systems When is using substitution best? When is using elimination (knock-out) the best?. When we solve systems, we could have different types of solutions, or more specifically, numbers of solutions

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3.3.2 – Types of Solutions

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  1. 3.3.2 – Types of Solutions

  2. Using elimination or substitution, we have found 2 ways to solve systems • When is using substitution best? • When is using elimination (knock-out) the best?

  3. When we solve systems, we could have different types of solutions, or more specifically, numbers of solutions • We can tell the # of solutions based on elimination by looking for 1 of two things

  4. How to Tell # of Solutions • A) 1 solution; if you can solve for x and y, and both x and y work for the given system of equations • B) Infinite solutions; if you knock out a variable, and everything cancels, and it makes sense (IE 3 = 3 doesn’t make sense) • C) Zero solutions; if you knock out a variable and everything cancels, and it DOES NOT make sense (IE 3 = -10)

  5. Example. Tell how many solutions exist to the system. If one solution exists, find the values of x and y. • 4x + y = -4 • 3x + y = -1

  6. Example. Tell how many solutions exist to the system. If one solution exists, find the values of x and y. • -4x + 8y = -12 • 2x – 4y = 7

  7. Example. Tell how many solutions exist to the system. If one solution exists, find the values of x and y. • 2x – y = 4 • 4x – 2y = 8

  8. Working together, solve the following 3 systems. • 1) • 8x + 14y = 4 • -6x – 7y = -10 • 2) • 7x + 2y = 24 • 8x + 2y = 30 • 3) • 2x + 8y = 6 • -5x – 20y = -15

  9. Word Problems • We can also use elimination when writing word problems • Example. An online store is older albums for download, a pack of 5 for $5 and a pack of 10 for $8. You buy 45 albums to download for $37. How many of each pack did you buy?

  10. Example. A can of Coke costs $0.75, while a can of Dr. Pepper costs $0.50. You buy 40 cans total and spend $26.25. Find the number of Coke cans you bought.

  11. Assignment • Pg. 143 • 27-32, 34, 36, 37, • Pg. 11 • 14, 15

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