3.1 Solving Linear Systems by Graphing Objective: solve a system of linear equations in two variables by graphing.

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3.1 Solving Linear Systems by Graphing Objective: solve a system of linear equations in two variables by graphing

What are systems of linear equations?

Systems of Linear Equations A system of two linear equations in two variables x and y consists of two equations. The coefficients of the terms in the equations can be any real numbers 3x – y = 3Equation 1 x + 2y = 8Equation 2 A solution of a system of two linear equations in two variables is an ordered pair (x,y) that satisfies both equations. When you graph the system, the solution is represented by the point (or points) of intersection of the two lines.

Solve a System by Graphing y = -x +3 y = 2x + 9

Solve a System by Graphing 3x – y = 3 x + 2y = 8

Solve a System by Graphing x – 3y = 1 -x + y = -1

Solutions of Systems It is also possible for a system to have infinitely many solutions or no solution. You can find out how many solutions a linear system has by graphing each equation and analyzing the graphs.

Number of Solutions of a Linear System Exactly One Solution: – The graph of the system is a pair of lines that intersect in one point. – the lines have different slopes – the system has exactly one solution Infinitely Many Solutions: – The graph of the system is a pair of identical lines – The lines have the same slope and the same y-intercept – The system has infinitely many solutions No Solution: – The graph of the system is a pair of parallel lines – The lines have the same slope and different y-intercepts – The system has no solution

Number of Solutions of a Linear System Exactly One SolutionInfinitely Many Solutions No Solution

Tell how many solutions the linear system has. 2x – y = 1 -4x + 2y = -2

Tell how many solutions the linear system has. x + 2y = 4 x + 2y = 1

Tell how many solutions the linear system has. x – 5y = 5 x + 5y = 5

Basketball Christie played in a basketball game in which she scored a total of 21 points. In the game, she made twice as many two-point shots as three- point shots. How many of each type of shot did Christie make?