Exercise 25 Page 217

Notice that the y-variable has opposite coefficients in both equations. If we add the equations, the y-terms will be eliminated. Therefore, we will use the Elimination Method. Let's add Equation (I) to Equation (II), then solve for x.

x+y=4 & (I) x-y=4 & (II)

SysEqnAdd

(II): Add (I)

x+y=4 x-y+( x+y)=4+( 4)

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(II):Solve for x

RemovePar

(II): Remove parentheses

x+y=4 x-y+x+y=4+4

AddTerms

(II): Add terms

x+y=4 2x=8

DivEqn

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

x+y=4 2x/2=8/2

MovePartNumRight

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

x+y=4 2/2 * x=8/2

QuotOne

(II): a/a=1

x+y=4 1 * x=8/2

IdPropMult

(II): Identity Property of Multiplication

x+y=4 x=8/2

CalcQuot

(II): Calculate quotient

x+y=4 x=4

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

x+y=4 x=4

Substitute

(I): x= 4

4+y=4 x=4

SubEqn

(I): LHS-4=RHS-4

4+y-4=4-4 x=4

SubTerms

(I): Subtract terms

y=0 x=4

The solution, or point of intersection, of the system of equations is (4,0).