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Warm Up Evaluate each expression for x = 1 and y =–3. 1. x – 4 y 2. –2 x + y

Warm Up Evaluate each expression for x = 1 and y =–3. 1. x – 4 y 2. –2 x + y Write each expression in slope-intercept form, then then graph. 3. y – x = 1 4. 2 x + 3 y = 6 5. 0 = 5 y + 5 x. 13. –5. y = x + 1. y = x + 2. y = – x. y = x + 1. y = x + 2. y = – x.

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Warm Up Evaluate each expression for x = 1 and y =–3. 1. x – 4 y 2. –2 x + y

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  1. Warm Up Evaluate each expression for x = 1 and y =–3. 1.x – 4y2. –2x + y Write each expression in slope-intercept form, then then graph. 3.y –x = 1 4. 2x + 3y =6 5. 0 = 5y + 5x 13 –5 y = x +1 y =x + 2 y = –x

  2. y = x +1 y =x + 2 y = –x

  3. Solving Linear Systems by Graphing

  4. Objectives Identify solutions of linear equations in two variables. Solve systems of linear equations in two variables by graphing. Vocabulary systems of linear equations solution of a system of linear equations

  5. Copy in TINA A system of linear equations is a set of two or more linear equations containing two or more variables. A solution of a system of linear equations with two variables is an ordered pair that satisfies each equation in the system. So, if an ordered pair is a solution, it will make both equations true.

  6. 3x – y 13 3(5) – 2 13 0 2 – 2 0 15 – 2 13 0 0  13 13  Copy in TINA Identifying Solutions of Systems Tell whether the ordered pair is a solution of the given system. (5, 2); 3x – y = 13 Substitute 5 for x and 2 for y in each equation in the system. The ordered pair (5, 2) makes both equations true. (5, 2) is the solution of the system.

  7. Helpful Hint If an ordered pair does not satisfy the first equation in the system, there is no reason to check the other equations.

  8. –x + y = 2 x + 3y = 4 –(–2) + 2 2 –2 + 3(2) 4 4 2 –2 + 6 4 4 4 Copy in TINA Identifying Solutions of Systems Tell whether the ordered pair is a solution of the given system. x + 3y = 4 (–2, 2); –x + y = 2 Substitute –2 for x and 2 for y in each equation in the system.  The ordered pair (–2, 2) makes one equation true but not the other. (–2, 2) is not a solution of the system.

  9. 2x + y = 5 (1, 3); –2x + y = 1 2x + y = 5 –2x + y = 1 2(1) + 3 5 –2(1) + 3 1 –2 + 3 1 2 + 3 5  1 1 5 5  Copy in TINA Try This! Tell whether the ordered pair is a solution of the given system. Substitute 1 for x and 3 for y in each equation in the system. The ordered pair (1, 3) makes both equations true. (1, 3) is the solution of the system.

  10. y = 2x – 1 y = –x + 5 Copy in TINA All solutions of a linear equation are on its graph. To find a solution of a system of linear equations, you need a point that each line has in common. In other words, you need their point of intersection. The point (2, 3) is where the two lines intersect and is a solution of both equations, so (2, 3) is the solution of the systems.

  11. Helpful Hint Sometimes it is difficult to tell exactly where the lines cross when you solve by graphing. It is good to confirm your answer by substituting it into both equations.

  12. Check Substitute (–1, –1) into the system. y = –2x– 3 y = x (–1) (–1) (–1)–2(–1)–3 –12– 3 –1 –1  –1 – 1  Copy in TINA Solving a System of Equations by Graphing Solve the system by graphing. Check your answer. y = x Graph the system. y = –2x – 3 The solution appears to be at (–1, –1). y = x (–1, –1) y = –2x – 3 (–1, –1) is the solution of the system.

  13. y = x + 5 y = x+ 5 y = –2x– 1 3–2+ 5 3 –2(–2)– 1 y = –2x – 1 3 3 3 4 – 1   3 3 Copy in TINA Try This! Solve the system by graphing. Check your answer. y = –2x – 1 Graph the system. y = x + 5 The solution appears to be (–2, 3). Check Substitute (–2, 3) into the system. (–2, 3) is the solution of the system.

  14. Lesson Quiz Tell whether the ordered pair is a solution of the given system. 1. (–3, 1); 2. (2, –4); no yes Solve the system by graphing. 3. y + 2x = 9 (2, 5) y = 4x – 3

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