Review Homework Pages 37-38. QuestionParallelPerpendicular 1y=2xy=-0.5x+2.5 2 3y=-4x+6 4.Neither 5.Perpendicular 6.Neither 7.Parallel Page 37.

Review Homework

•Pages 37-38

4.Neither5.Perpendicular6.Neither7.Parallel

Page 37

8) Part aa.y=2xb.y=-0.5x+7.5c.y=2x+3

Part c a⊥bb⊥ ca∥c

Page 38

Part c a⊥bb⊥ ca∥c

8) Part aa.y=2xb.y=-0.5x+7.5c.y=2x+3

Page 38

page 38 Diagonals of a square• The two diagonals are congruent (same length). • Each diagonal bisects the other. In other words,

the point where the diagonals intersect(cross), divides each diagonal into two equal parts

• Each diagonal divides the square into two congruent isosceles right triangles. Because the triangles are congruent, they have the same area, and each triangle has half the area of the square.

1-3 Solving Systems of Equations by Graphing (page 40)

• A SYSTEM OF EQUATIONS ( 연립방정식 )is a group of two or more equations.

• When the system of equations are lines, they are called linear systems.

• A solution ( 해 ) of a system of linear equations in two variables is an ordered pair (x,y) that is a solution to each equation.

• In order to find the solution, you graph both lines and see where they intersect ( 교점 ). The point where they intersect is their solution.

• No Solution ( 해가 없다 ) when both lines are parallel (same slope, different y-intercepts)

• Infinite Number of Solutions when both lines are the same lines (same slope and same y-intercept) INFINITELY MANY SOLUTIONS ( 해가 무한히 많다 )

• In order to determine if a point is a solution, substitute it into the equations and see if it is true.

Example• Solve the system by graphing:y=x+2y=-2x+2

Solutiony=x+2 y=-2x+2

• The lines intersect at (0,2) so that is our solution BUT we MUST check and see if it is correct.

• Check by substituting the solution back into the original equations.

y=x+2 y=-2x+2 2 = 0+2 2=-2(0)+2 2=2 2=2So (0,2) is the solution to the system of equations.

Try these page 43-44 #1-3

1. 3x+4y=12, 2x+4y=82. x+2y=10, 2x+4y=103. 2x+4y =12, y = (-½)x+3

Don’t forget to check your answers!

1. Check (4,0)3x+4y=12 2x+4y=83(4) + 4(0) =12 2(4) + 4(0) = 8 12= 12 8=8

2. They are parallel so there is NO SOLUTION!

3. They are the same line so every point on the lines is a solution. Therefore, there are infinitely many solutions.

Classifying Systems• Meet in Point – Consistent –

independent• Parallel – Inconsistent –

Independent• Same – Consistent - Dependent

Change the second paragraphIf there is exactly one solution, the system is independent

toIf the lines are different, the system is independent.

Determining if an ordered pair is a solution

• Substitute the ordered pair into both equations and see if the solutions are true. If they are true, the ordered pair is a solution. if the ordered pair gives a false solution in either equation, the ordered pair does not satisfy the system of equations.

• Try page 44 # 4 and 5• 3x+2y=4, -x+3y=-5 (2,-1), (-3,2) • 2x+y=4, 4x+3y=9 (5/2 ,2), (3/2 ,1)

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Homework

•Page 45-46