Solving Systems Using Substitution

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Presentation transcript:

Solving Systems Using Substitution

Old MacDonald had a farm…or maybe a ranch? Old MacDonald takes care of chickens and cows. How many, you ask? Pfft… He’s not going to tell you that!

Jerk You do know this, however: The number of chickens is three less than five times the number of cows. There are a total of 50 legs on his farm…not including his.

Let y = number of chickens Try to write an equation for each: Cool info, bro Let x = number of cows Let y = number of chickens Try to write an equation for each: The number of chicken is three less than five times the number of cows. There are a total of 50 legs on his farm…not including his. y = 5x – 3 4x + 2y = 50

Wouldn’t bribing him have been easier? Now we have a system of equations. Work with your partner and brainstorm ways you could solve it. Try something!

Solving Systems by Substitution There are multiple ways to solve this system, but we are going to focus on a very straight-forward method… SUBSTITUTION!

So y must be 5x – 3 in the other equation as well Listen carefully! This means “y is 5x – 3” Remember that in a system of equations, you want to know where the x and y coordinates are the same so… So y must be 5x – 3 in the other equation as well y = 5x – 3 4x + 2y = 50

Copy this down carefully! y = 5x – 3 4x + 2y = 50 y = 5x – 3 4x + 2y = 50 y = 5x – 3 y = 5(4) – 3 y = 20 – 3 y = 17 4x + 2y = 50 4(4) + 2y = 50 16 + 2y = 50 –16 –16 . 2y = 34 2 2 y = 17 4x + 2( ) = 50 4x + 10x – 6 = 50 14x – 6 = 50 +6 +6 . 14x = 56 14 14 x = 4 (4, 17)

Old MacDonald has four cows and seventeen chickens on his farm. Answer in a sentence… (4, 17) Who or what are we talking about, what does the x-coordinate mean, and what does the y-coordinate mean? Old MacDonald has four cows and seventeen chickens on his farm.

Substitution When one variable in one equation is alone (isolated, solved for), you can substitute its equivalent expression into the other equation and solve for the remaining variable.

Work on the problems on the back with your partner! Your Turn! Work on the problems on the back with your partner!