DashboardNewsSettingsHelp
Get Premium
Dashboard
Dashboard Sign out
Pearson Algebra 2 Common Core, 2011
PA
Pearson Algebra 2 Common Core, 2011 View details
5. Systems With Three Variables
Continue to next subchapter

Exercise 40 Page 172

When using the Substitution Method to solve a system of equations, it is necessary to isolate a variable.

(-1,2,0)

Practice makes perfect

The given system consists of equations of planes. We will use the Substitution Method to solve a system of equations. When using this method, it is necessary to isolate a variable. In the third equation, it will be easier to isolate x.

4y+2x=6-3z & (I) x+z-2y=-5 & (II) x-2z=3y-7 & (III)
AddEqn

(III): LHS+2z=RHS+2z

4y+2x=6-3z x+z-2y=-5 x=3y-7+2z

With a variable isolated in one of the equations, we can substitute its equivalent expression into the remaining equations. In the final step of the simplification of these substitutions, our goal is to have yet another variable isolated.

4y+2x=6-3z x+z-2y=-5 x=3y-7+2z

(I), (II): x= 3y-7+2z

4y+2( 3y-7+2z)=6-3z 3y-7+2z+z-2y=-5 x=3y-7+2z
â–¼
(I), (II): Simplify
Distr

(I): Distribute 2

4y+6y-14+4z=6-3z 3y-7+2z+z-2y=-5 x=3y-7+2z

(I), (II): Add and subtract terms

10y-14+4z=6-3z y+3z-7=-5 x=3y-7+2z
AddEqn

(II): LHS+7=RHS+7

10y-14+4z=6-3z y+3z=2 x=3y-7+2z
SubEqn

(II): LHS-3z=RHS-3z

10y-14+4z=6-3z y=2-3z x=3y-7+2z

This time, the y-variable was isolated in the second equation. We can now substitute its equivalent expression into the first equation.

10y-14+4z=6-3z y=2-3z x=3y-7+2z
â–¼
(I): Solve by substitution
Substitute

(I): y= 2-3z

10( 2-3z)-14+4z=6-3z y=2-3z x=3y-7+2z
Distr

(I): Distribute 10

20-30z-14+4z=6-3z y=2-3z x=3y-7+2z
AddSubTerms

(I): Add and subtract terms

6-26z=6-3z y=2-3z x=3y-7+2z
SubEqn

(I): LHS-6=RHS-6

-26z=-3z y=2-3z x=3y-7+2z
AddEqn

(I):LHS+3z=RHS+3z

-23z=0 y=2-3z x=3y-7+2z
DivEqn

(I): .LHS /(-23).=.RHS /(-23).

z=0 y=2-3z x=3y-7+2z

The value of z is 0. Substituting 0 for z into the second equation, we can find the value of y.

z=0 y=2-3z x=3y-7+2z
Substitute

(II): z= 0

z=0 y=2-3( 0) x=3y-7+2z
ZeroPropMult

(II): Zero Property of Multiplication

z=0 y=2 x=3y-7+2z

Now that we know the values of y and z, we are able to find the value of x.

z=0 y=2 x=3y-7+2z
SubstituteII

(III): y= 2, z= 0

z=0 y=2 x=3( 2)-7+2( 0)
â–¼
(III): Simplify
Multiply

(III): Multiply

z=0 y=2 x=6-7+0
AddSubTerms

(III): Add and subtract terms

z=0 y=2 x=-1

The solution to the system is the point (-1,2,0). This is the singular point at which all three planes intersect.

Subchapter links expand_more
arrow_right Lesson Check p.171
1
2
3
Lesson Check 4 (Page 171)
Lesson Check 5 (Page 171)
6
Lesson Check 7 (Page 171)
8
arrow_right Practice and Problem-Solving Exercises p.171-173
Practice and Problem-Solving Exercises 9 (Page 171)
Practice and Problem-Solving Exercises 10 (Page 171)
Practice and Problem-Solving Exercises 11 (Page 171)
Practice and Problem-Solving Exercises 12 (Page 171)
Practice and Problem-Solving Exercises 13 (Page 171)
Practice and Problem-Solving Exercises 14 (Page 171)
Practice and Problem-Solving Exercises 15 (Page 171)
Practice and Problem-Solving Exercises 16 (Page 171)
Practice and Problem-Solving Exercises 17 (Page 171)
Practice and Problem-Solving Exercises 18 (Page 171)
Practice and Problem-Solving Exercises 19 (Page 171)
Practice and Problem-Solving Exercises 20 (Page 171)
21
Practice and Problem-Solving Exercises 22 (Page 172)
Practice and Problem-Solving Exercises 23 (Page 172)
Practice and Problem-Solving Exercises 24 (Page 172)
Practice and Problem-Solving Exercises 25 (Page 172)
Practice and Problem-Solving Exercises 26 (Page 172)
Practice and Problem-Solving Exercises 27 (Page 172)
Practice and Problem-Solving Exercises 28 (Page 172)
Practice and Problem-Solving Exercises 29 (Page 172)
30
31
32
Practice and Problem-Solving Exercises 33 (Page 172)
Practice and Problem-Solving Exercises 34 (Page 172)
Practice and Problem-Solving Exercises 35 (Page 172)
Practice and Problem-Solving Exercises 36 (Page 172)
Practice and Problem-Solving Exercises 37 (Page 172)
Practice and Problem-Solving Exercises 38 (Page 172)
Practice and Problem-Solving Exercises 39 (Page 172)
Practice and Problem-Solving Exercises 40 (Page 172)
Practice and Problem-Solving Exercises 41 (Page 172)
Practice and Problem-Solving Exercises 42 (Page 172)
Practice and Problem-Solving Exercises 43 (Page 173)
Practice and Problem-Solving Exercises 44 (Page 173)
45
arrow_right Standardized Test Prep p.173
Standardized Test Prep 46 (Page 173)
47
Standardized Test Prep 48 (Page 173)
49
arrow_right Mixed Review p.173
Mixed Review 50 (Page 173)
Mixed Review 51 (Page 173)
Mixed Review 52 (Page 173)
Mixed Review 53 (Page 173)
Mixed Review 54 (Page 173)
Mixed Review 55 (Page 173)
Mixed Review 56 (Page 173)