warm up solve for y: 2y-6x=3. solving systems of equations a system of equations-is a set of two or...

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!3 2

2 11

y x

x y

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?

x Y=1.5x Y=12-2.5x

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.)

2 12x y 3 2 4x y