Warm up Solve for y: 2y-6x=3. Solving systems of equations A system of equations-is a set of two or more equations that have variables in common. When.

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Presentation transcript:

Warm up Solve for y: 2y-6x=3

Solving systems of equations A system of equations-is a set of two or more equations that have variables in common. When solving systems of equations you look for a solution that makes each equation true

Graphing Systems of Equations

Solve For solution by graphing Verify by plugging intersection point into each equations

Solve by graphing Verify by plugging intersection point into each equations

Solving! Verify by plugging intersection point into each equations

Ellen leaves the trailhead at dawn to hike 12 mi toward the lake, where as her friend Maria is camping. At the same time, Maria starts her hike toward the trailhead. Ellen is walking uphill so she averages only 1.5 miles per hour, while Maria averages 2.5 miles per hour walking downhill. When and where will they meet?

xY=1.5xY=12-2.5x

Warm up. Solve the system of equations by graphing

Dislikes/Disadvantages of Graphing?

Substitution The substitution method is used to eliminate one of the variables by replacement when solving a system of equations. Think of it as "grabbing" what one variable equals from one equation and "plugging" it into the other equation.

Solve by Substitution Ex1) y=-1 y=x-5

Solve by substitution Ex 2) y=4x+5 Y=-3x-9

Solve by substitution Ex 3) -7x-5y=-1 X-5y=23

Substitution

Which method would you use and why?

Determine which method you would use and then solve Y-4=-2x

Number of Solutions? One Solution: Infinite Solutions: No Solutions: Explain how these situations can happen, show a graph of two equations that represent each scenarios. (Just graph, you do not need to come up with specific equations.)

Suppose there is a piggybank that contains 57 coins, which are only quarters and dimes. The total value of these coins is $9.45. Determine how many of the coins are quarters and how many are dimes. Substitution