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Algebra

Algebra. 7.1 Solving Linear Systems by Graphing. System of Linear Equations (linear systems). Two equations with two variables. An example: 4x + 5y = 3 2x = 6y -10 A solution to a linear system is an ordered pair (x, y) that, when substituted in, makes both equations true.

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Algebra

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  1. Algebra 7.1 Solving Linear Systems by Graphing

  2. System of Linear Equations(linear systems) • Two equations with two variables. An example: 4x + 5y = 3 2x = 6y -10 • A solution to a linear system is an ordered pair (x, y) that, when substituted in, makes both equations true. • Thus, the solution would be on both graphs. The solution(s) is the intersection of the lines.

  3. Is the ordered pair a solution to the system of equations? Yes or no. • -2x + y = -11 (6, 1) -x – 9y = 15 Plug it in and check! -2(6) + (1) = -11? -12 + 1 = -11? -11 = -11 Yes. -(6) – 9(1) = 15? -6 – 9 = 15? -15 = 15? No. The point is not a solution to the system of equations.

  4. Use the graph to find the solution to the system of equations. Then check your solution algebraically. • y = 3x -12 y = -2x + 3 The solution seems to be (3, -3). Check this solution algebraically on your paper. Who can check it on the board? Yes. The point is a solution to the system.

  5. Steps to “Graphing to Solve a Linear System” • Write each equation in a form that is easy to graph (Slope-int or standard) • Graph both equations on the same coordinate plane • Find the point of intersection • Check the point algebraically in the system of equations

  6. Solve the system graphically. Check the solution algebraically. • 3x – 4y = 12 -x + 5y = -26 Step 1) Put the equations in a graph-able form. 3x – 4y = 12 Find the x-int. and y-int. 3(0) – 4y = 12 -4y = 12 y = -3 The y-int is (0, -3) Graph it! 3x – 4(0) = 12 3x = 12 x = 4 The x-int is (4, 0) Graph it! Put -x + 5y = -26 into slope-int form. +x +x 5y = x – 26 y = 1/5 x – 5 1/5 The solution to the system seems to be (-4, -6) . . . .

  7. Check (-4, -6) in the system algebraically. • 3x - 4y = 12 (-4, -6) -x + 5y = -26 3(-4) - 4(-6) = 12? -12 + 24 = 12? 12 = 12 Yes. -(-4) + 5(-6) = -26? 4 – 30 = -26? -26 = -26 Yes. The point is a solution to the system of equations.

  8. You try! Solve the system graphically. Check the solution algebraically. . . • 3x + y = 11 x - 2y = 6 Step 1) Put the equations in a graph-able form. 3x + y = 11 Put into slope-int form. -3x -3x y = -3x + 11 Graph it! x - 2y = 6 Put into slope-int form. -x -x -2y = -x + 6 y = 1/2 x – 3 Graph it! The solution to the system seems to be (4, -1) . . .

  9. Check (4, -1) in the system algebraically. • 6x + 2y = 22 (4, -1) x - 2y = 6 6(4) + 2(-1) = 22? 24 - 2 = 22? 22 = 22 Yes. (4) - 2(-1) = 6? 4 + 2 = 6? 6 = 6 Yes. The point is a solution to the system of equations.

  10. HW • P. 401-403 #11-19 Odd, 25-33 Odd, 47-59 Odd

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