Exercise 36 Page 383

Notice that the y-coefficient is the same in both equations. If we subtract the equations, the y-terms will be eliminated. Therefore, we will use the Elimination Method. Let's subtract Equation (I) from Equation (II), then solve for x.

x+y=1.5 & (I) 2x+y=1 & (II)

SysEqnSub

(II): Subtract I

x+y=1.5 2x+y-( x+y)=1- 1.5

Distr

(II): Distribute -1

x+y=1.5 2x+y-x-y=1-1.5

AddSubTerms

(II): Add and subtract terms

x+y=1.5 x=-0.5

Now that we have found a solution for x, we can substitute it into our first equation to solve for y.

x+y=1.5 x=-0.5

Substitute

(I): x= -0.5

-0.5+y =1.5 x=-0.5

AddEqn

(I): LHS+0.5=RHS+0.5

y =2 x=-0.5

The solution to the system — the point of intersection — is (- 0.5, 2).