Bellwork 1/27 Solve the following by: y = 2x y = x + 3 1.) Substitution 2.) Graphing (Use an old graph paper)

Bellwork 1/27 y = 2x y = x + 3 2x = x + 3 (Subtract x) x = 3 and since y = 2x y = 2(3) y = 6 Solution is (3,6)

Graph y = 2x & y = x + 3 y = x + 3 Y y = 2x X Solution= (3,6)

Bellwork 1/28 Solve the following by: x - y = 2 2x + y = 1 1.) Substitution 2.) Graphing (Use an old graph paper)

Bellwork 1/28 x - y = 2 & 2x + y = 1 2x + y = 1 (Solve for y) 2x - 2x + y = -2x + 1 y = - 2x + 1 x - (-2x + 1) = 2 (Substitute)

Bellwork 1/28 x - (-2x + 1) = 2 x + 2x - 1 = 2 3x - 1 = 2 3x = 3 x = 1

Bellwork 1/28 y = - 2(1) + 1 y = -2 + 1 y = -1 Solution (1,-1)

Graph x - y = 2 & 2x + y = 1 y = x - 2 & y = -2x + 1 Solution= (1,-1)

Lets Graph this new equation Check this out Now Consider what happens when we add the two equations y = 2x y = x + 3 Lets Graph this new equation 2y = 3x + 3

How does this graph compare with the other two? Graph 2y = 3x + 3 or y = 3/2x + 3/2 Y How does this graph compare with the other two? X y = 3/2x +3/2

Graph 2y = 3x + 3 y = -2/3x + 4 Y y = 2x X Notice that the graph passes thru the point of intersection Solution= (3,6)

Objective To be able to solve a system of equations by using the linear combination (add) method

1.) Solve by Addition (elimination) 2x + 3y = 7 x - 3y = 8 (Divide by 3) 3x = 15 x = 5

1.) Solve by Addition (elimination) 2x + 3y = 7 2(5) + 3y = 7 10 + 3y = 7 Solution (5,-1) (Subtract 10) 3y = -3 (Divide by 3 y = -1

2.) Solve by Addition (elimination) 3a = 2b + 7 2b = 9 - a Notice that the like terms of the two equations do not line up. 3a - 2b = 7 a + 2b = 9 Rearrange them and THEN add

2.) Solve by Addition (elimination) 3a - 2b = 7 a +2b = 9 (Divide by 4) 4a = 16 a = 4

2.) Solve by Addition (elimination) Now Substitute back into one of the equations 2b = 9 - a 2b = 9 -(4) 2b = 5 b = 5/2 Solution (4, 5/2)

3.) You try This one 2x - y = 7 x+ y = 2 (Divide by 3) 3x = 9 x = 3

3.) You try this one x + y = 2 (3) + y = 2 y = -1 (Subtract 3) Solution (3,-1)

Be ready to answer 1.) What are the other two methods of solving two equations? 2.) What do you do, before you add, if the terms of the equation aren’t lined up?

Classwork On a separate sheet of paper show the work for: Worksheet 7-3 Homework Page 363 (1-16)

How many solutions do the following equations have? 1.) x = 3y 2x - y = 5 2.) 8x - 4y = -32 -2x + y = 8 One (3,1) Many

How many solutions do the following equations have? 1.) y = 3x -2 3y + 2 = 9x 2.) y = 1/4x + 3 8y - 3x = 12 None One (12,6)

1.) y = 3x + 4 Graph y = mx + b Y-intercept Slope Bellwork 1/31 (3 slides) Graph y = mx + b 1.) y = 3x + 4 Y-intercept Slope 1 of 3

2.) 2x + y = -1 Graph y = mx + b Y-intercept Slope Bellwork 1/31 (3 slides) Graph y = mx + b 2.) 2x + y = -1 Y-intercept Slope 2 of 3

3.) -2x - y = - 5 Graph y = mx + b Y-intercept Slope Bellwork 1/31 (2 slides) Graph y = mx + b 3.) -2x - y = - 5 Y-intercept Slope 3 of 3

Graph y = 3x + 4 Y X

Graph 2x + y = -1 y = -2x + -1 Y X

Graph -2x - y = -5 y = -2x + 5 Y X

Classwork Solve the following by: y = 2x y = x + 3 1.) Graphing 2.) Substitution 3.) Linear Combination (+) Show all your Work

Graph y = 2x & y = x + 3 y = x + 3 Y y = 2x X Solution= (3,6)

Classwork (Sub) y = 2x y = x + 3 2x = x + 3 (Subtract x) x = 3 and since y = 2x y = 2(3) y = 6 Solution is (3,6)

Classwork (L.C.) y = 2x y = x + 3 (multiply by -1) -y = -x - 3 y = 2x(rewrite 1st equation & add) 0 = x - 3 (Add the equations) x = 3

Classwork (L.C.) Since x = 3, then y = 2(3) y = 6 Solution ( 3,6)

Classwork (1 of 3) Solve the following by: y = -x + 3 y = x + 1 1.) Graphing 2.) Substitution 3.) Linear Combination (+) Show all your Work

Classwork (2 of 3) Solve the following by: 3x - y = 0 y = 6 1.) Graphing 2.) Substitution 3.) Linear Combination (+) Show all your Work

Classwork (3 of 3) Solve the following by: x - y = 4 x + y = 12 1.) Graphing 2.) Substitution 3.) Linear Combination (+) Show all your Work

Classwork 1 of 3) (1 , 2) 2 of 3) (2 , 6) 3 of 3) (8 , 4)

Homework Page 373 (2-20 even)