body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

Dashboard

Big Ideas Math: Modeling Real Life, Grade 8 View details

3. Solving Systems of Linear Equations by Elimination

Finish the assignment

Continue to next subchapter

Exercise 1 Page 212

The Elimination Method can be used to solve a system of linear equations if either of the variable terms would cancel out the corresponding variable term in the other equation when added together.

(5,1)

Practice makes perfect

To solve a system of linear equations using the Elimination Method, one of the variable terms needs to be eliminated when one equation is added to or subtracted from the other. This means that either the x- or the y-terms must cancel each other out. 2 x- y=9 & (I) 4 x+ y=21 & (II) We can see that the y-terms will eliminate each other if we add Equation (I) to Equation (II).

2x-y=9 4x+y=21

SysEqnAdd

(II): Add (I)

2x-y=9 4x+y+( 2x-y)=21+( 9)

▼

(II):Solve for x

RemovePar

(II): Remove parentheses

2x-y=9 4x+y+2x-y=21+9

AddSubTerms

(II): Add and subtract terms

2x-y=9 6x=30

DivEqn

(II): .LHS /6.=.RHS /6.

2x-y=9 6x/6=30/6

MovePartNumRight

(II): a* b/c=a/c* b

2x-y=9 6/6 * x=30/6

QuotOne

(II): a/a=1

2x-y=9 1 * x=30/6

IdPropMult

(II): Identity Property of Multiplication

2x-y=9 x=30/6

CalcQuot

(II): Calculate quotient

2x-y=9 x=5

Now, we can solve for y by substituting the value of x into either equation and simplifying.

2x-y=9 x=5

Substitute

(I): x= 5

2( 5)-y=9 x=5

▼

(I):Solve for y

Multiply

(I): Multiply

10-y=9 x=5

SubEqn

(I): LHS-10=RHS-10

10-y-10=9-10 x=5

SubTerms

Subtract terms

- y=-1 x=5

MultEqn

(I): LHS * (-1)=RHS* (-1)

-1(- y)=-1(-1) x=5

MultPropNegOne

(I): Multiplication Property of -1

y=1 x=5

The solution, or point of intersection, of the system of equations is (5,1). To check this solution, we will substitute it back into the given system and simplify. If doing so results in true statements for every equation in the system, our solution is correct.

2x-y=9 4x+y=21

(I), (II): x= 5, y= 1

2( 5)- 1 ? = 9 4( 5)+ 1 ? = 21

(I), (II): Multiply

10-1 ? = 9 20+1 ? = 21

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

9 = 9 ✓ 21 = 21 ✓

Subchapter links

Try It p.212-214

Self-Assessment for Concepts & Skills p.214

Self-Assessment for Problem Solving p.215

Review & Refresh p.216

Concepts, Skills, & Problem Solving p.216-218

Exercise 1 Page 212

Hints

Check the answer

Practice exercises

Assess your skill