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3.1: Solving Linear Systems by Graphing Group 4

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Get two variables, (x,y), to correctly come out of two equations ax+by=c dx+ey=f Check whether the ordered pair is a solution of the system. Brittany Lawson KoolkidsMath Group 4

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Example 1: Is (2,2) and (0,1) solutions of: 3x-2y=2 X+2y=6 Put variables (2,2) into equations: 3 (2)-2 (2)=2* 2 + 2 (2)=6* Because both variables solve both equations It is a Solution of the System Brittany Lawson Group 4

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Example 2: Put variables (0,1) into equations: 3(0)-2(1)=2 * 0+2(1)=-2≠6 Because Equation 2 does not check It is not a Solution of the System Brittany Lawson Group 4

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Goal: To solve a system of equations graphically, graph both equations and see where they intersect. The intersection point is the solution Example 1: 4x-6y=12 2x+2y=6 Solve for y= mx+b to graph 4x-6y=12 2x+2y=6 4x=6y+12 2y=-2x+6 4x-12=6y y= x+ 6y=4x-12 y=-x+3 y= x- y= x-2 Graph y= x-2 and y=-x+3 Brittany Lawson Group 4

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The point of intersection of the two lines (3,0) is the solution to the system of equations. This means that (3,0), when substituted into either equation, will make them both true. Use the check method to check your answer. 4x-6y=12 4(3)-6(0)=12 2x+2y=6 2(3)+2(0)=6 Solution of Systems

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Systems with Many Solutions Example 1: 3x-2y=6 6x-4y=12 Graph the equation (Solving each equation for y). 3x-2y=6 y= x-3 6x-4y=12 y= x-3 The graph of the equation is the Same line. So Infinitely there are many solutions. Brittany Lawson Group 4

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Systems with No Solutions Example 2: -x+5y=8 2x-10y=7 Graph the equations solving for y. The lines are parallel and do not intersect So, There is no solution. Brittany Lawson Group 4

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Checking Solutions of Linear Equations Is the ordered pair (1, 3) a solution of the given system of equations? 3x + 5y = 18 x – 3y = –8 3x+5y=18 X-3y=-8 3(1) + 5(3) = 18 3 + 15 = 18 18 = 18 1 – 3(3) = –8 1 – 9 = –8 –8 = – 8 Solution of Equations Brittany Lawson Group 4

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Solving a System of Equations Graphically x – y = 4 3x + y = 0 y = x – 4 y = –3x You should check that (1, –3) is actually a solution to both equations. Brittany Lawson Group 4

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