Exercise 69 Page 227

To determine which point satisfies both equations, we will have to solve the system of linear equations.
3 x-5 y=11 & (I) 3 x-8 y=5 & (II) We can see that the x-terms will eliminate each other if we subtract (I) from (II). This means we will use the Elimination Method.

3x-5y=11 3x-8y=5

SysEqnSub

(II): Subtract (I)

3x-5y=11 3x-8y-( 3x-5y)=5- 11

▼

(II):Solve for x

Distr

(II): Distribute - 1

3x-5y=11 3x-8y-3x+5y=5-11

AddSubTerms

(II): Add and subtract terms

3x-5y=11 - 3y=- 6

DivEqn

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

3x-5y=11 y=2

We found that y=2. Paying attention to the possible solutions, we see that the only one whose y-value is 2, is choice C.