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Chapter 7 sec.2

Chapter 7 sec.2. How do I solve a system of equations by substitution?. Two equations together are called a system of equations . A solution of a system of equations is an ordered pair that satisfies both equations. A system of equations can have 0, 1 or an infinite number of solutions.

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Chapter 7 sec.2

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  1. Chapter 7 sec.2 How do I solve a system of equations by substitution?

  2. Two equations together are called a system of equations . • A solution of a system of equations is an ordered pair that satisfies both equations. • A system of equations can have 0, 1 or an infinite number of solutions

  3. i • Steps: • Get x or y alone on one side of the equal sign • Substitute the solution into the other equation and solve. • Substitute that solution into either equation and solve.

  4. To use substitution: Ex: y = 3x x+2y = -21 Since y is already isolated, in the 2nd equation substitute (3x) for y. Part 1Part 2 x + 2(3x) = -21 use -3 for x in either equation x + 6x = -21 y = 3(-3) 7x = -21 y = -9 x = -3 solution (-3, -9)

  5. Ex. X + 5y = -3 (subtract 5y from each side) 3x – 2y = 8 Isolate one of the variables on one side of the equal sign. I chose to isolate the x in the 1st equation. Part 1 Part 2 X = -5y – 3 (substitute into the 2nd Eq.) x + 5(-1) = -3 3(-5y-3)-2y = 8 x + -5 = -3 -15y-9-2y = 8 x = 2 -17y = 17 Y= -1 (choose an equation to substitute into) solution (2,-1)

  6. Ex 6x – 2y = -4 Y = 3x + 2 (already isolated….yeah) substitute into the 1st equation. Part 1 6x – 2(3x + 2) = -4 6x – 6x – 4 = -4 -4 = -4 Statement is true………………..solution is: infinitely many If your statement is false…….solution is: no solution

  7. Ex. A metal alloy is 25% copper. Another metal alloy is 50% copper. How much of each should be used to make 1000 gallons of a metal alloy that is 45% copper? The system is: a + b + 1000 and .25a + .50b = 45(1000) Use substitution to solve the system. SHOW YOUR WORK! 25% copper 50% copper 45% copper Total grams a b 1000 Grams of copper 0.25a 0.50b 0.45(1000)

  8. SOLUTION: a + b = 1000I chose to isolate the a. (subtract b from each side) .25a + .50b = .45(1000) Part 1Part 2 a = 1000 – b a + 800 = 1000 .25(1000 – b) + .50b = 450 a = 200 250 - .25b + .50b = 450 250 + .25b = 450 .25b = 200 b= 800 (substitute into either equation)

  9. So…….. a = 200 b = 800 Means…… You need 200 gallons of 25% copper And 800 gallons of a 50% copper

  10. Practice: • Y = 5x 2x + 3y = 34 • 8x + 2y = 13 4x + y = 11 • X = 1/2y + 3 2x – y = 6

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