Exercise 1 Page 168

Since neither equation has a variable with a coefficient of 1, we will use the Elimination Method. In this exercise, this means that either the x-terms or the y-terms must cancel each other out. 2 x-3 y=9 & (I) 4 x+3 y=9 & (II)
We can see that the y-terms will eliminate each other if we add (I) to (II).

2x-3y=9 4x+3y=9

SysEqnAdd

(II): Add (I)

2x-3y=9 4x+3y+( 2x-3y)=9+ 9

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(II):Solve for x

AddSubTerms

(II): Add and subtract terms

2x-3y=9 6x=18

DivEqn

(II): .LHS /6.=.RHS /6.

2x-3y=9 x=3

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

2x-3y=9 x=3

Substitute

(I): x= 3

2( 3)-3y=9 x=3

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(I):Solve for y

Multiply

(I): Multiply

6-3y=9 x=3

SubEqn

(I): LHS-6=RHS-6

-3y=3 x=3

DivEqn

(I): .LHS /(- 3).=.RHS /(- 3).

y=- 1 x=3

The solution, or intersection point, of the system of equations is (3,-1).