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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

3. Proving Triangles Congruent-SSS, SAS

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Exercise 37 Page 361

Eliminate b from the equations.

D

Practice makes perfect

Let's use the Elimination Method to solve the given system of equations. Since we are asked to find a, let's eliminate b.

4a+6b=6 & (I) -2a+b=-7 & (II)

(II): LHS * 6=RHS* 6

4a+6b=6 -12a+6b=-42

(I): Subtract (II)

4a+6b-( -12a+6b)=6-( -42) -12a+6b=-42

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(I): Solve for a

(I): a-(- b)=a+b

4a+6b-(-12a+6b)=6+42 -12a+6b=-42

(I): Remove parentheses

4a+6b+12a-6b=6+42 -12a+6b=-42

(I): Add and subtract terms

16a=48 -12a+6b=-42

(I): .LHS /16.=.RHS /16.

a=3 -12a+6b=-42

Since we are only asked to find a, we can stop here. Since a=3, the correct choice is D.

Extra

Finding b

If you are also interested in b, you can substitute a=3 in the second equation and solve the resulting equation for b.

a=3 & (I) -12a+6b=-42 & (II)

(II):a= 3

a=3 -12( 3)+6b=-42

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(II): Solve for b

(II): (- a)b = - ab

a=3 -36+6b=-42

(II): LHS+36=RHS+36

a=3 6b=-6

.LHS /6.=.RHS /6.

a=3 b=-1

Subchapter links

Exercises p.357-361