Math Flashcards for lesson 7

Subtraction- y=3x+2 y=x-4

-3x+y=2 -3x+y=2 -x+y=-4 (-) -x+y=-4 -2x=6 -2x/-2=6/-2 x=-3 y=(-3)-4 y=-7 (-3,-7)

Substitution- y=-x+8 y=4x-7

-8=-x-y +y -y-x=-8 +y 7=4x-y -x=-8+y -x/-1=x -8+y/-1= 8-y x=8-y y-4x=7 +13 -13-4x=7 +13 y-4(8-y)=7 -4x=20 y-32-4y=7 -4x/-4=x 20/-4=-5 +32 -32-3y=7 +32 x=-5 -3y=39 (-5,-13 -3y/-3=y 39/-3=-13)

Multiplication- -8=-x-y 7=4x-7

-8=-x-y 4(-y-x=-8) 7=4x-y -4y-4x=32 - y-4x=7 5y=-25 5y/5=y -25/5=-5 y=-5 +5 -5-4x=7 +5 -4x=12 -4x/-4=x 12/-4=-3 x=-3 (-3,-5)

Addition- 2x+y=-4 5x+3y=-6

2x+4y=-4 5(2x+4y=-4) 5x+3y=-6 2(5x+3y=-6) 10x+20y=-20 (-) 10x+6y=-12 14y=-8 14y/14=8/14 y=4/7 2x+4(4/7)=-4 -16/7 2x+16/7=-4 -16/7 2x/2=6 3/7/2 x=3 3/14 (3 3/14,4/7)

Substitution- 2x+y=-4 5x+3y=-6

2x+y=-4 -2x x+y=-4 -2x 5x+3y=-6 y=-4-2x 2(-6)+y=-4 +12 -12+y=-4 +12 y=8 5x+3y=-6 5x+3(-4-2x)=-6 +12 5x-12-6x=-6 -x/-1=x 6/-1=-6 x=-6 (-6,8)

Multiplication- 2x+y=-4 5x+3y

2x+y=-4 3(2x+y=-4) 5x+3y=-6 6x+3y=-12 - 5x+3y=-6 x=-6 2(6)+y=-4 -12 12+y=-4 -12 y=-16 (3,-16)

Substitution- 2x+y=3 4x+2y=6

2x+y=3 +-2x 2x+y=3 +-2x 4x+2y=6 y=3-2x 4x+2(3-2x)=6 +-6 4x+6-4x=6 +-6 4-4x=0 0=0

Subtraction- 2x+y=3 4x+2y=6

2x+y=3 2(2x+y=3) 4x+2y=6 - 4x+2y=6 4x+2y=6 0+0=0 0=0

Multiplication- 2x+y=3 4x+2y=6

2x+y=3 2(2x+y=3) 4x+2y=6 4x+2y=6 - 4x+2y=6 0+0=0 0=0 Infanite

Subtraction- y=3x-4 y=-3x-4

4=3x-y 4=3x-y 4=-3x-y 4=-3-y 8=-2y 8/-4 -2y/-2=y y=-4 4=3x-y -4 3x-=(-4) -4 0=3x 0/3=0 3x/3=x x=0 (0,-4)

Addition- -8=-y-x 7=-x-y

y-4x=7 5x=-1 -4-x=-8 5x/5=x -1/5= -1/5 y+4(1/5)=7 +4/5 y-4/5=7 +4/5 y=7 4/5 (-1/5,7 4/5)

Substitution- y=2x+1 y=2x-2

y=2x+1 -2x 2x+1=2x-2 -2x y=2x-2 1 doesnt equal -2 No Solution

Subtraction- y=2x+1 y=2x-2

y=2x+1 -2x+y=1 y=2x-2 - -2x+y=-2 0+0=-1 0 doesnt equal -1 No solution

Multiplication-y=2x+1 y=2x-2

y=2x+1 1(-2x+y=1) y=2x-2 -2x+y=-2 -2x+y=1 - -2x+y=-2 0+0=-1 0 doesnt equal -1 No Solution

Substitution- y=3x-4 y=3x-4

y=3x-4 +-3x 4=3x-y +-3x y=-3x-4 4=-3x+y 4=3(-1/3)-y +1 4=-1-y +1 5=-y -y/-1=y 5/-1=-5 4=-3x-y -5 4=-3x-(-5) -5 -1=-3x -1/-3= 1/3 -3x/-3=x\ x=1/3 (1/3,-5)

Substitution- y=3x-4 y=-3x-4

y=3x-4 +3 -3x-4=3x-4 +3 y=-3x-4 +4 -4=6x-4 +4 0=6x 0/6=0 6x/6=x x=0 y=3(0)-4 y=0-4 -4=y (0,-4)

Multiplication- y=3x-4 y=-3x-4

y=3x-4 -1(-3x+y=-4) y=-3x-4 3x+y=-4 3x+-y=4 - 3x+y=-4 -2y=8 -2y/-2=y 8/2=4 y=4 +4 -4=3x-4 +4 0=3x 0/3=0 3x/3=x (0,-4)

Substitution- y=x+2 y=2x+1

y=x+2 +-2 x+2=2x+1 +-2 y=2x+1 -x x=2x+-1 -x +1 0=x+-1 +1 1=x y=1+2 y=3 y=x+2 3=1+2 3=3 (1,3)

Subtraction- y=x+2 y=2x+1

y=x+2 -x+y=2 y=2x+1 -2x+y=1 x+0=1 x=1 y=1+2 y=3 y=x+2 3=1+2 (1,3) 3=3

Multiplication- y+2 y=2x+1

y=x+2 2(-x+y=2) y=2x+1 -2x+y=1 -2x+2y=4 - -2x+y=1 y=3 +-2 3=x+2 +-2 1=x (1,3) y=x+2 3=1+2 3=3