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3.2: Solutions to Linear Equations

Objectives: *Find solutions to linear equations in two variables. *Decide if an ordered pair is a solution to a linear equation in two variables. 3.2: Solutions to Linear Equations. Solving an Equation.

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3.2: Solutions to Linear Equations

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  1. Objectives: *Find solutions to linear equations in two variables. *Decide if an ordered pair is a solution to a linear equation in two variables. 3.2: Solutions to Linear Equations

  2. Solving an Equation • If you know one coordinate in an ordered pair that is a solution for an equation, you can find the other coordinate through substitution and solving the resulting equation.

  3. –8 + 8 + 4y = 4 + 8 (add 8 to both sides) Example Complete the ordered pair (4, ) so that it is a solution of –2x + 4y = 4. Let x = 4 in the equation and solve for y. –2x + 4y = 4 –2(4) + 4y = 4 (replace x with 4) –8 + 4y = 4 (compute the product) 4y = 12 (simplify both sides) y = 3 (divide both sides by 4) So the completed ordered pair is (4, 3).

  4. 4x + 2 – 2 = 4 – 2 (subtract 2 from both sides) Example Complete the ordered pair (__, – 2) so that it is a solution of 4x – y = 4. Let y = – 2 in the equation and solve for x. 4x – y = 4 4x– (– 2) = 4 (replace y with – 2) 4x + 2 = 4 (simplify left side) 4x = 2 (simplify both sides) x = ½ (divide both sides by 4) So the completed ordered pair is (½, – 2).

  5. Problem Set 3.2 (TB pp. 168-169) Complete the given ordered pairs. 3.) 3x + 4y = 12 (0, ), ( ,0), (-4, ) 3 4 6 3x + 4y = 12 4y = -3x + 12 4 4 y = -3x + 12 4 If x = 0 y = -3 (0) + 12 4 y = 3 If x = -4 y = -3 (-4) + 12 4 x = 6 3x + 4y = 12 3x = -4y + 12 3 3 x = -4y + 12 3 If y = 0 x = -4 (0) + 12 3 x = 4

  6. Problem Set 3.2 (TB pp. 168-169) Complete the given ordered pairs. 9.) x = -5 ( ,4), ( , -3), ( ,0) 17. Complete the table. 2x – y = 4 -5 -5 -5 2x – y = 4 2x = 4 + y 2 2 x = 4 + y 2 If y = 0 x = 4 + 0 2 x = 2 If y = 2 x = 4 + 2 2 x = 3 2 3 -2 -10 If x = -3 y = 2(-3) – 4 y = -10 If x = 1 y = 2(1) – 4 y = -2 2x – 4 = y 2x - 4 = y y = 2x - 4

  7. Problem Set 3.2 (TB pp. 168-169) Tell which of the given ordered pairs are solutions. 23.) y = 7x - 2 (1,5), (0,-2), (-2,-16) (1,5) 5 = 7(1) -2 5 = 7 – 2 5 = 5 (1,5) is a solution (0,-2) -2 = 7(0) -2 -2 = 0 – 2 -2 = -2 (0,-2) is a solution (-2, -16) -16 = 7(-2) -2 -16 = -14 – 2 -16 = -16 (-2,-16) is a solution

  8. Problem Set 3.2 (TB pp. 168-169) • 33. Janai earns $12 per hour working as a math tutor. We • can express the amount she earns each week, y, for • working x hours with the equation y = 12x. Indicate with • a yes or no which of the following could be one of Janai’s • paychecks. If you answer no, explain your answer. • $60 for working 5 hours • $100 for working 9 hours • $80 for working 7 hours • $168 for working 14 hours y = 12x; 60 = 12(5) 60 = 60, Yes. y = 12x; 100 = 12(9) 100 ≠ 108, No. she should earn $108 for working 9 hours y = 12x; 80 = 12(7) 80 ≠ 84, No. she should earn $84 for working 7 hours y = 12x; 168 = 12(14) 168 = 168, Yes

  9. Problem Set 3.2 (TB pp. 168-169) Individual Practice: Homework Even Numbers Nos. 2, 4, 6…36

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