Bellwork1/26 Solve by Graphing: x + 2y = 7 x + y = 1.

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Presentation transcript:

Bellwork1/26 Solve by Graphing: x + 2y = 7 x + y = 1

1st Change to y = mx + b x + y = 1 y = -x + 1 x + 2y = 7 x-x+2y=-x+7

y = -1/2x + 7/2 y = -x + 1 Y 7/2 = 3 1/2 X (-5,6) Notice the intersection is not at 2 pts.

To be able to solve a system of equations by substitution…. Objective To be able to solve a system of equations by substitution….

1.) Solve by Substitution y = 3x - 1 2x + y = 9 So…... 2x + (3x-1) = 9 5x - 1 = 9 (add 2x and 3x) 5x = 10 (add 1 to both sides) x = 2 (divide both by 5)

1.) Solve by Substitution Since x = 2 We can now substitute it back in y = 3x - 1 (the 1st equation) y = 3(2) -1(put in the x value) y = 6 - 1 (solve for y) y = 5 (2,5) is the solution

1.) Solve by Substitution Or …. x = 2 We can substitute it in the other one 2x + y = 9 (the 2nd equation) 2(2) + y = 9(put in the x value) 4 + y = 9(subtract 4 from both) y = 5 (solve for y)

Graph y = 3x -1 & 2x + y = 9 2x+y=9 Y y = 3x - 1 X Solution= (2,5)

2.) Solve by Substitution 2x + 3y = 7 y + 1 = x So….. 2(y+1) + 3y = 7 2y +2 + 3y = 7(distribute the 2) 5y + 2 = 7(Add 2y & 3y) 5y = 5 & y = 1(divide both by5)

2.) Solve by Substitution Since y = 1 We can now substitute it back in y + 1 = x (the 2nd equation) 1 + 1 = x (put in the y value) 2 = x (solve for x) (2,1) is the solution

Solve by Substitution y = 3x You try this one y + 4x = 28 First find what x or y equals Then Substitute into the other equation. You try this one

Solve by Substitution y = 3x y + 4x = 28 3x + 4x = 28 7x = 28 x = 4 Since x = 4 y = 3x y = 3(4) y = 12 solution (4,12)

3.) Solve by Substitution First solve for x or y 2x + 4y = 8 3x + 5y = 14 1st… 2x = -4y + 8 (Subtract 4y) x = -2y + 4 (Divide by 2) Now substitute for x 3(-2y + 4) + 5y = 14

3.) Solve by Substitution 3(-2y + 4) + 5y = 14 -6y + 12 + 5y = 14 -y + 12 = 14 -y = 2 so…. y = -2

3.) Solve by Substitution Since y = -2 and x = -2y + 4 Then x = -2(-2) + 4 x = 4 + 4 x = 8 Solution (8,-2)

Classwork Do worksheet 7.2 You must use a separate sheet of paper to show the work!!!

Homework Page 356 (1-4 all, 6-28 even)