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.

Big Ideas Math: Modeling Real Life, Grade 8

BI

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

2. Solving Systems of Linear Equations by Substitution

Continue to next subchapter

Exercise 14 Page 209

Does either of the equations have an isolated variable or an isolated term in it?

(4,2.5)

Practice makes perfect

When solving a system of equations using the Substitution Method, there are three steps.

Isolate a term in one of the equations.
Substitute the expression for that term into the other equation and solve.
Substitute this solution into one of the equations and solve for the value of the other variable.

It looks like it will be simplest to isolate 4y in the first equation. x+4y=14 ⇔ 4y=14-xNow that we have isolated 4y, we can solve the system by substitution.

4y=14-x & (I) 3x+4y=22 & (II)

(II):4y= 14-x

4y=14-x 3x+ (14-x)=22

(II): Remove parentheses

4y=14-x 3x+14-x=22

▼

(II): Subtract term

CommutativePropAdd

(II): Commutative Property of Addition

4y=14-x 3x-x+14=22

(II): Subtract term

4y=14-x 2x+14=22

(II): LHS-14=RHS-14

4y=14-x 2x+14-14=22-14

(II): Subtract terms

4y=14-x 2x=8

Now, we can use the Division Property of Equality to simplify the equation even further.

4y=14-x 2x=8

(II): .LHS /2.=.RHS /2.

4y=14-x 2x2= 82

▼

(II): Calculate quotient

MovePartNumRight

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

4y=14-x 22x= 82

(II): Calculate quotient

4y=14-x 1x=4

(II): Identity Property of Multiplication

4y=14-x x=4

Great! Now, to find the value of y, we need to substitute x=4 into the first equation.

4y=14-x x=4

(I): x= 4

4y=14- 4 x=4

(I): Subtract term

4y=10 x=4

(I): .LHS /4.=.RHS /4.

4y4= 104 x=4

MoveRightFacToNumOne

(I): 1/b* a = a/b

44y= 104 x=4

(I): Calculate quotient

1y=2.5 x=4

(I): Identity Property of Multiplication

y=2.5 x=4

The solution, or point of intersection, to this system of equations is the point (4,2.5).

Checking Our Answer

To check our answer, we will substitute our solution into both equations. If doing so results in true statements, then our solution is correct.

x+4y=14 & (I) 3x+4y=22 & (II)

(I), (II): x= 4, y= 2.5

4+4( 2.5)? =14 3( 4)+4( 2.5)? =22

(I), (II): Multiply

4+10? =14 12+10? =22

(I), (II): Add terms

14=14 ✓ 22=22 ✓

Because both equations are true statements, we know that our solution is correct.

Subchapter links

Try It p.206-207

Self-Assessment for Concepts & Skills p.207

Self-Assessment for Problem Solving p.208

Review & Refresh p.209

Concepts, Skills, & Problem Solving p.209-210