Exercise 11 Page 209

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

(- 6.5,- 3)

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.

For this exercise, 2x is already isolated in one equation, so we can skip straight to solving!

2x=y-10 & (I) 2x+7=2y & (II)

Substitute

(II):2x= y-10

2x=y-10 y-10+7=2y

AddTerms

(II): Add terms

2x=y-10 y-3=2y

SubEqn

(II): LHS-y=RHS-y

2x=y-10 y-3-y=2y-y

▼

(II): Subtract term

CommutativePropAdd

(II): Commutative Property of Addition

2x=y-10 y-y-3=2y-y

SubTerm

(II): Subtract term

2x=y-10 - 3=y

RearrangeEqn

(II): Rearrange equation

2x=y-10 y=- 3

Great! Now, to find the value of x, we need to substitute y=- 3 into the second equation.

2x=y-10 y=- 3

Substitute

(I): y= - 3

2x= - 3-10 y=- 3

SubTerm

(I): Subtract term

2x=- 13 y=- 3

DivEqn

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

2x2= - 132 y=- 3

▼

(I): Simplify left-hand side

MovePartNumRight

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

22x= - 132 y=- 3

CalcQuot

(I): Calculate quotient

1x= - 132 y=- 3

IdPropMult

(I): Identity Property of Multiplication

x= - 132 y=- 3

▼

(I): Simplify left-hand side

MoveNegNumToFrac

(I): Put minus sign in front of fraction

x=- 132 y=- 3

CalcQuot

(I): Calculate quotient

x=- 6.5 y=- 3

The solution, or point of intersection, to this system of equations is the point (- 6.5,- 3).

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.

2x=y-10 & (I) 2x+7=2y & (II)

(I), (II): x= - 6.5, y= - 3

2( - 6.5)? = - 3-10 2( - 6.5)+7? =2( - 3)

(I), (II): - a(- b)=a* b

- 2(6.5)? =- 3-10 -2(6.5)+7? =- 2(3)

(I), (II): Multiply

- 13? =- 3-10 - 13+7? =- 6

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

- 13=- 13 ✓ - 6=- 6 ✓

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

Hints

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Practice exercises

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Checking Our Answer