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Identify solutions of linear equations in two variables.

Objectives. Identify solutions of linear equations in two variables. Solve systems of linear equations in two variables by graphing.

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Identify solutions of linear equations in two variables.

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  1. Objectives Identify solutions of linear equations in two variables. Solve systems of linear equations in two variables by graphing.

  2. 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. System of Equations: The point where two lines intersect.

  3. 3x – y 13 3(5) – 2 13 0 2 – 2 0 15 – 2 13 0 0  13 13  Example 1A: Identifying Systems of Solutions 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.

  4. –x + y = 2 x + 3y = 4 –(–2) + 2 2 –2 + 3(2) 4 4 2 –2 + 6 4 4 4 Example 1B: Identifying Systems of Solutions 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.

  5. 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 Check It Out! Example 1a 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.

  6. x– 2y = 4 3x + y = 6 3(2)+(–1) 6 2 – 2(–1) 4 6 – 1 6 2 + 2 4  5 6 4 4 Check It Out! Example 1b Tell whether the ordered pair is a solution of the given system. x –2y = 4 (2, –1); 3x + y = 6 Substitute 2 for x and –1 for y in each equation in the system. The ordered pair (2, –1) makes one equation true, but not the other. (2, –1) is not a solution of the system.

  7. y = 2x – 1 y = –x + 5 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.

  8. Check Substitute (–1, –1) into the system. y = –2x– 3 y = x (–1) (–1) (–1)–2(–1)–3  –12– 3 –1 –1  –1 – 1 Example 2A: Solving a System 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.

  9. 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 Check It Out! Example 2a 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.

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