Exercise 27 Page 229

In this system of equations, at least one of the variables has a coefficient of 1. Therefore, we will approach its solution with the Substitution Method. When solving a system of equations using the Substitution Method, there are three steps.

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

Observing the given equations, it looks like it will be simplest to isolate y in the first equation.

- 2x+y=- 2 & (I) 3x+y=3 & (II)

AddEqn

(I): LHS+2x=RHS+2x

- 2x+y+2x=- 2+2x 3x+y=3

AddTerms

(I): Add terms

y=- 2+2x 3x+y=3

Now that we have isolated y, we can solve the system by substitution.

y=- 2+2x & (I) 3x+y=3 & (II)

Substitute

(II):y= - 2+2x

y=- 2+2x 3x+( - 2+2x)=3

▼

Solve for x

Distr

(II): Distribute 1

y=- 2+2x 3x+(- 2)+2x=3

AddNeg

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

y=- 2+2x 3x-2+2x=3

AddTerms

(II): Add terms

y=- 2+2x 5x-2=3

AddEqn

(II):LHS+2=RHS+2

y=- 2+2x 5x-2+2=3+2

AddTerms

(II): Add terms

y=- 2+2x 5x=5

DivEqn

(II): .LHS /5.=.RHS /5.

y=- 2+2x 5x5= 55

CancelCommonFac

(II): Cancel out common factors

y=- 2+2x 5x5= 55

SimpQuot

(II): Simplify quotient

y=- 2+2x x= 55

QuotOne

(II): a/a=1

y=- 2+2x x=1

Great! Now to find the value of y, we need to substitute x=1 into Equation (I).

y=- 2+2x & (I) x=1 & (II)

Substitute

(I):x= 1

y=- 2 +2( 1) x=1

(I): Multiply

y=- 2 +2 x=1

AddTerms

(I): Add terms

y=0 x=1

The solution, or point of intersection, to this system of equations is the point (1,0).