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Lesson 7-2

Lesson 7-2. Substitution. Transparency 2. Click the mouse button or press the Space Bar to display the answers. Transparency 2a. Objectives. Solve systems of equations by using subtraction Solve real-world problems involving systems of equations. Vocabulary.

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Lesson 7-2

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  1. Lesson 7-2 Substitution

  2. Transparency 2 Click the mouse button or press the Space Bar to display the answers.

  3. Transparency 2a

  4. Objectives • Solve systems of equations by using subtraction • Solve real-world problems involving systems of equations

  5. Vocabulary • Substitution - putting the value of one variable (in terms of the other variable) into the equation

  6. Substitution • We have used substitution before, plugging in a constant value for x to find y in a equation of a line.y = 4 x – 7 let x =3 then y = 4(3) – 7 = 12 – 7 = 5 • Now we are using substitution to help us eliminate a variable in a system of equations (to solve them)y = 4 x – 7 and y = 2 x + 9by substituting what y is (in terms of x) in the second equation for y in the first equation we get2 x + 9 = 4 x – 7  an equation of just one variable! • We can solve this to get x = 8 and y = 25

  7. Use to find the value of x. Use substitution to solve the system of equations. Since substitute 4y for x in the second equation. Second equation Simplify. Simplify. Combine like terms. Divide each side by 15. Simplify. Example 1 Answer: The solution is (20, 5).

  8. Use substitution to solve the system of equations. First equation Subtract 4x from each side. Simplify. Example 2 Solve the first equation for y since the coefficient of y is 1.

  9. Second equation Distributive Property Combine like terms. Add 36 to each side. Simplify. Divide each side by 10. Simplify. Example 2 cont Find the value of x by substituting 12 – 2x for y in the second equation.

  10. First equation Simplify. Subtract 20from each side. Answer: The solution is(5, –8).The graph verifies the solution. Example 2 cont Substitute 5 for x in either equation to find the value of y.

  11. Use substitution to solve the system of equations. Second equation Subtract x from each side. Simplify. Substitute for y in the first equation. First equation Distributive Property Simplify. Example 3 Solve the second equation for y. Answer: The statement -4 = 8 is false. This means there are no solutions of the system of equations. That is, the graphs of the lines are parallel.

  12. Gold Gold is alloyed with different metals to make it hard enough to be used in jewelry. The amount of gold present in a gold alloy is measured in 24ths called karats. 24-karat gold is or 100% gold. Similarly, 18- karat gold is or 75% gold. How many ounces of 18-karat gold should be added to an amount of 12-karat gold to make 4 ounces of 14-karat gold? Example 4

  13. Let the number of ounces of 18-karat gold and the number of ounces of 12-karat gold. Use the tableto organize the information. 18-karat gold 12-karat gold 14-karat gold Total Ounces x y 4 Ounces of Gold The system of equations is and Use substitution to solve this system. Example 4 cont

  14. First equation Combine like terms. Subtract y from each side. Simplify. Second equation Distributive Property Example 4 cont

  15. Subtract 3 from each side. Simplify. Multiply each side by –4. Simplify. Example 4 cont

  16. First equation Subtract from each side. Simplify. Answer: ounces of the 18-karat gold and ounces of the 12-karat gold should be used. Example 4 cont

  17. Summary & Homework • Summary: • In a system of equations, solve one equation for a variable, and then substitute that expression into the second equation to solve • Homework: • Pg 379 12-28 even

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