Review Homework Pages 37-38

QuestionParallelPerpendicular 1y=2xy=-0.5x y=-4x+6 4.Neither 5.Perpendicular 6.Neither 7.Parallel Page 37

8) Part a a.y=2x b.y=-0.5x+7.5 c.y=2x+3 Part c a ⊥ b b ⊥ c a ∥ c Page 38

Part c a ⊥ b b ⊥ c a ∥ c 8) Part a a.y=2x b.y=-0.5x+7.5 c.y=2x+3 Page 38

page 38 Diagonals of a square The two diagonals are congruent (same length).congruent Each diagonal bisects the other. In other words, the point where the diagonals intersect(cross), divides each diagonal into two equal partsbisectsintersect 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.congruentisoscelesright trianglesarea

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+2 y=-2x+2

Solution y=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=2  So (0,2) is the solution to the system of equations.

Try these page # x+4y=12, 2x+4y=8 2.x+2y=10, 2x+4y=10 3.2x+4y =12, y = (-½)x+3 Don’t forget to check your answers!

1.Check (4,0) 3x+4y=12 2x+4y=8 3(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 paragraph If there is exactly one solution, the system is independent to If 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) o x x o

Homework Page 45-46