3.8 SOLVING EQUATIONS AND FORMULAS SWBAT •  To Solve Equa/ons for Given Variables •  Use Formulas for Real World Problems. Solving For Variables… •  The equa/ons we have dealt with have had only one type variable. 1
x+5= 4
2
2y + 5 = 4y + 5
•  Equa/ons can have two or more different variables. 1
y = x+5
y
=
2
•  Some we know as Formulas. y = mx + b
2
x −2
a2 + b2 = c2
A = lw
Solving Equations for SpeciGic Variables… •  Treat the equa/on as you would any other. UNDO opera/ons! •  You know the variable is solved for when it is isolated on one side of the equa/on, equal to everything else. •  Watch the videos below and copy into your notes. VIDEO 1 VIDEO 2 VIDEO 3 Ex1: Solving Equations for SpeciGic Variables •  Solve for y 3x − 4y = 8
3x − 4y − 3x = 8 − 3x
−4y = −3x + 8
−4y −3x + 8
=
−4
−4
3
y = x−2
4
Ex1B: Solving Equations for SpeciGic Variables •  Solve for x 3x − 4y = 8
3x − 4y + 4y = 8 + 4y
3x = 4y + 8
3x 4y + 8
=
3
3
4
8
x = y−
3
3
You try! 1.
2. You try! 3.
4. Ex2: Solving Equations for SpeciGic Variables Solve for m. 2m − t = sm + 5
2m − t − sm = sm + 5 − sm
2m − t − sm + t = 5 + t
2m − sm = 5 + t
m (2 − s) = 5 + t
m (2 − s) 5 + t
=
2−s
2−s
5+t
m=
2−s
Use the Reverse of the Distribu/ve Property! Ex2B: Solving Equations for SpeciGic Variables 7x − 2z = 4 − xy
7x − 2z + xy = 4 − xy + xy
7x − 2z + xy + 2z = 4 + 2z
7x + xy = 4 + 2z
x ( 7 + y ) = 4 + 2z
x ( 7 + y) 4 + 2z
=
7+ y
7+ y
Use the Reverse of the Distribu/ve Property! 4 + 2z
x=
7+ y
You try… 1.
2.