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Algebra 1 UNIT 5 Function Form & Solutions of systems of equations

Learn to rewrite equations in function form, find solutions using graphs, and identify system solutions. Practice problems included.

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Algebra 1 UNIT 5 Function Form & Solutions of systems of equations

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  1. Algebra 1UNIT 5Function Form & Solutions of systems of equations OBJECTIVES: Solve equations for y so that y is a function of x. Find the solution of a system of equations given a graph.

  2. Vocabulary Function Form– An equation solved for y so that y is a function of x. • Example: y = -7x + 3 • Non-example: -4x + 2y = 5 • System of equations – Two or more equations. • Example: y = 2x – 4 3x - 4y = 5 • Non-example: y = 2x – 4

  3. #1 Rewriting an Equation in Function Form Rewrite the equation so y is a function of x. 6y - 12x = 18 6y - 12x = 18 +12x +12xAdd 12x to both sides 6y = 12x + 18 ______ ________ ________ 6 6 6 Divide each term by 6 y = 2 x + 3

  4. #2 Rewriting an Equation in Function Form Rewrite the equation so y is a function of x. --3y + 2x = 15 -3y + 2x = 15 -2x -2xSubtract 2x to both sides -3y = -2x + 15 ______ _______ _______ -3 -3 -3 Divide each term by -3

  5. Practice Problems 1) 2)

  6. #3 y x • (-2, -1) is the only point where both equations have the same x and y value! Solution of a system of equation given a graph Solution is where the lines intersect Where do they intersect? (-2, -1) Therefore, (-2,-1) is the solution!

  7. #4 Finding the solution to the system of equations by graphing. y Where do they intersect? (-2, 3) x

  8. y x You try: Find the solution to the system of equations by graphing. Where do they intersect? (1, 2)

  9. Vocabulary • No solution to a system of equations – The two lines do not cross or touch at any point. The lines are parallel. • Many solutions to a system of equations – The two lines intersect at all points. The two lines graph as the exact same line.

  10. y x 5. What happens if the lines never meet? Will the lines ever intersect? No Is there a solution? NO

  11. y x 6. What happens if the lines are the same? Will the lines intersect? Yes! Does the system have a solution? All real numbers orinfinite number of solutions

  12. 7. Is (2,-1) a solution of the system of equations? The coordinate must satisfy both equations (A) (B) Yes, (2,-1) is a solution (A) (B) (2,-1) is the point where the lines intersect on the graph

  13. 8. Is (-2,1) a solution of the system of equations? YOU TRY!! The coordinate must satisfy both equations (A) (B) No, (2,-1) is not a solution (A) (B) Since (A) is no, we don’t need to plug the point into (B)

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