7.4 Applications of Linear Systems (Pages 396 403) – You can solve systems of equations using graphing, substitution, or elimination. Graphing works best when the y intercept is between -10 and 10, and the slope is a whole number or fraction between -10 and 10. Substitution works well when you have either an x or y variable with a coefficient of 1 or -1. works for any system. Elimination Steps for solving linear systems word problems. Define your variables-write them our so you and your teachers understand what you mean. What are we trying to find or relate? Write your equations. Choose a method to solve the equations. You have a pocket full of quarters and dimes. You count the number of coins and find you have 45. You find the amount your coins are worth and find you have $5.40. How many dimes and how many quarters do you have? Define your variables: Let d = number of dimes, let q = number of quarters What are we trying to find or relate? Number of each type of coin Value of $5.40 Write your equations. d + q = 45 .10d + .25q = 5.40 Choose a method to solve the equations. I will use elimination. So I will multiply the first equation by -.10. -.10(d + q = 45) -.10d + -.10q = -4.50 Solve. -.10d -.10q = -4.50 .10d + .25q = 5.40 Add equations .15q = .90 Divide .15 .15 q = 6 d + q = 45 d + 6 = 45 Subtract 6 -6 -6 d = 39 You have 6 quarters and 39 dimes.
7.4 Applications of Linear Systems (Pages 396 – 403) You can solve systems of equations using graphing, substitution, or elimination. Graphing works best when the y intercept is between -10 and 10, and the slope is a whole number or fraction between -10 and 10. Substitution works well when you have either an x or y variable with a coefficient of 1 or -1. Elimination works for any system. Steps for solving linear systems word problems. Define your variables-write them our so you and your teachers understand what you mean. What are we trying to find or relate? Write your equations. Choose a method to solve the equations. You have a pocket full of quarters and dimes. You count the number of coins and find you have 45. You find the amount your coins are worth and find you have $5.40. How many dimes and how many quarters do you have? Define your variables: Let d = number of dimes, let q = number of quarters What are we trying to find or relate? Number of each type of coin Value of $5.40 Write your equations. d + q = 45 .10d + .25q = 5.40 Choose a method to solve the equations. I will use elimination. So I will multiply the first equation by -.10. -.10(d + q = 45) -.10d + -.10q = -4.50 Solve. -.10d -.10q = -4.50 .10d + .25q = 5.40 Add equations .15q = .90 Divide .15 .15 q = 6 d + q = 45 d + 6 = 45 Subtract 6 -6 -6 d = 39 You have 6 quarters and 39 dimes.
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