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MTH 070 – Elementary Algebra

MTH 070 – Elementary Algebra. Chapter 4 Review. System of Equations. A set of two or more (related) equations. Solution: Values for the variables that make ALL of the equations true. 2 Equations w/ 2 unknowns … an ordered pair. 3 Equations w/ 3 unknowns … an ordered triple.

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MTH 070 – Elementary Algebra

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  1. MTH 070 – Elementary Algebra Chapter 4 Review

  2. System of Equations • A set of two or more (related) equations. • Solution: • Values for the variables that make ALL of the equations true. • 2 Equations w/ 2 unknowns … an ordered pair. • 3 Equations w/ 3 unknowns … an ordered triple. • Types of systems of two equations with two unknowns: • Two distinct intersecting lines • Consistent & Independent • Two distinct parallel lines • Inconsistent & Independent • Concurrent lines (i.e. equivalent equations) • Consistent & Dependent

  3. System of Equations Solving by Graphing • Graph both equations. • Determine the point of intersection (it’s the solution). • Write the solution as an ordered pair. • Check the solution in BOTH original equations.

  4. System of Equations Solving by Graphing

  5. System of Equations Solving by Substitution • Solve one of the equations for a variable. • Substitute the result of step 1 into the OTHER equation. • Solve the equation for the remaining variable. • Substitute the result of step 3 into the result of step 1. • Solve for the other variable. • Give the solution as an ordered pair. • Check the solution in BOTH original equations.

  6. System of Equations Solving by Substitution

  7. System of Equations Solving by Elimination • Put both equations into the same form. • Multiply each equation by numbers such that the resulting coefficients of y are opposites. • Add the equations (this will eliminate y). • Solve for x. • Repeat steps 2-3, swapping the roles of x and y. • Give the solution as an ordered pair. • Check the solution in BOTH original equations.

  8. System of Equations Solving by Elimination

  9. System of Equations Applications • Identify the unknowns. • Determine two equations that relate the unknowns. • Solve the system of equations. • Express your answer in terms of the problem (units?).

  10. System of Equations Applications The Gateway to the West Arch in St. Louis is 105 feet taller than the world’s tallest flagpole located in Panmunjon, North Korea. Find the height of each if the sum of their heights is 1,155 feet.

  11. System of Equations Applications – Mixture Problems • x = amount of first item w/ concentration, rate, or value of a. • y = amount of second item w/ concentration, rate, or value of b. • x + y = total amount • ax + by = final concentration or combined value

  12. System of Equations Applications – Mixture Problems How many gallons of a 20% salt solution must be mixed with 20 gallons of a 15% salt solution to obtain an 18% salt solution?

  13. System of Equations Applications – Mixture Problems • x = amount of first item w/ concentration, rate, or value of a. • y = amount of second item w/ concentration, rate, or value of b. • x + y = total amount • ax + by = final concentration or combined value Frozen peas sell for $1.99/lb and frozen carrots sell for $2.44/lb. The store wishes to provide a 2 pound bag of mixed vegetables that sells for $4.29. How much of each vegetable needs to go into this mix? Source: http://www.schwans.com

  14. System of Equations 3 Equations w/ 3 Unknowns • Use either substitution or elimination or a combination. • Substitution: Solve an equation for 1 variable, substitute into the other equations, solve the resulting system of 2 equ/2 unk, and substitute to determine the third variable. • Elimination: Add two equations to eliminate a variable, add two other equations to eliminate the same variable, & solve the resulting system of 2 equ/2 unk, and substitute to determine the third variable. • Express the answer as an ordered triple. • Check the solution in all 3 original equations.

  15. System of Equations 3 Equations w/ 3 Unknowns

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