Chapter 3.1, Problem 8WE

a

To determine

To Solve: The equation $2x+3y=7$

Answer to Problem 8WE

Final Answer: x = -2, y = $\frac{11}{3}$ ; x= 1, y = $\frac{5}{3}$ ; x = 3, y = $\frac{1}{3}$

Explanation of Solution

Given Information: We need to solve $2x+3y=7$ and it is given that domain of x is{-2,1,3}

Calculation: Since the domain of x is {-2,1,3}

So, when x = -2

By putting in $2x+3y=7$ , we have

  $-4+3y=7$

Or  $3y=11$

Or  $y=\frac{11}{3}$

When x = 1,

By putting in $2x+3y=7$ , we have

  $2+3y=7$

Or  $3y=5$

Or  $y=\frac{5}{3}$

When x = 3,

By putting in $2x+3y=7$ , we have

  $6+3y=7$

Or  $3y=1$

Or  $y=\frac{1}{3}$

b

To determine

To Solve: The equation $3x+6y=9$

Answer to Problem 8WE

Final Answer: x = -2 , y = $\frac{5}{2}$ ; x = 1, y = 1; x = 3, y = 0.

Explanation of Solution

Given Information:We need to solve $3x+6y=9$ and it is given that domain of x is{-2,1,3}

Calculation: Since the domain of x is {-2,1,3}

So, when x = -2

By putting in $3x+6y=9$ , we have

  $-6+6y=9$

Or  $6y=15$

Or  $y=\frac{5}{2}$

When x = 1,

By putting in $3x+6y=9$ , we have

  $3+6y=9$

Or  $6y=6$

Or  $y=1$

When x = 3,

By putting in $3x+6y=9$ , we have

  $9+6y=9$

Or  $6y=0$

Or  $y=0$

c

To determine

To Solve: The equation $-x-2y=0$

Answer to Problem 8WE

Final Answer: x = -2 , y = 1; x = 1, y = $\frac{-1}{2}$ ; x = 3, $y=\frac{-3}{2}$

Explanation of Solution

Given Information:We need to solve $-x-2y=0$ and it is given that domain of x is{-2,1,3}

Calculation: Since the domain of x is {-2,1,3}

So, when x = -2

By putting in $-x-2y=0$ , we have

  $2-2y=0$

Or  $-2y=-2$

Or  $y=1$

When x = 1,

By putting in $-x-2y=0$ , we have

  $-1-2y=0$

Or  $-2y=1$

Or  $y=\frac{-1}{2}$

When x = 3,

By putting in $-x-2y=0$ we have

  $-3-2y=0$

Or  $-2y=3$

Or  $y=\frac{-3}{2}$

d

To determine

To Solve: The equation $-2x+y=-3$

Answer to Problem 8WE

Final Answer: x = -2 , y = -7; x = 1, y = -1; x = 3, y = 3

Explanation of Solution

Given Information:We need to solve $-2x+y=-3$ and it is given that domain of x is{-2,1,3}

Calculation: Since the domain of x is {-2,1,3}

So, when x = -2

By putting in $-2x+y=-3$ , we have

  $4+y=-3$

Or  $y=-7$

When x = 1,

By putting in $-2x+y=-3$ ,we have

  $-2+y=-3$

Or  $y=-1$

When x = 3,

By putting in $-2x+y=-3$ , we have

  $-6+y=-3$

Or  $y=3$

e

To determine

To Solve: The equation $4x-9y=5$ .

Answer to Problem 8WE

Final Answer: x = -2 , y = $\frac{-13}{9}$ ; x = 1, y = $\frac{-1}{9}$ ; x = 3, $y=\frac{7}{9}$

Explanation of Solution

Given Information:We need to solve $4x-9y=5$ ,and it is given that domain of x is{-2,1,3}

Calculation: Since the domain of x is {-2,1,3}

So, when x = -2

By putting in $4x-9y=5$ ,we have

  $-8-9y=5$

Or  $-9y=13$

Or  $y=\frac{-13}{9}$

When x = 1,

By putting in $4x-9y=5$ , we have

  $4-9y=5$

Or  $-9y=1$

Or  $y=\frac{-1}{9}$

When x = 3,

By putting in $4x-9y=5$ ,we have

  $12-9y=5$

Or  $-9y=-7$

Or  $y=\frac{7}{9}$

f

To determine

To Solve: The equation $6x-\frac{1}{2}y=3$ .

Answer to Problem 8WE

Final Answer: x = -2 , y = -30; x = 1, y =6; x = 3, y =30

Explanation of Solution

Given Information:We need to solve $6x-\frac{1}{2}y=3$ and it is given that domain of x is {-2,1,3}.

Calculation: Since the domain of x is {-2,1,3}

So, when x = -2

By putting in $6x-\frac{1}{2}y=3$ , we have

  $-12-\frac{1}{2}y=3$

Or  $-\frac{1}{2}y=15$

Or  $y=-30$

When x = 1,

By putting in $6x-\frac{1}{2}y=3$ , we have

  $6-\frac{1}{2}y=3$

Or  $-\frac{1}{2}y=-3$

Or  $y=6$

When x = 3,

By putting in $6x-\frac{1}{2}y=3$ ,we have

  $18-\frac{1}{2}y=3$

Or  $-\frac{1}{2}y=-15$

Or  $y=30$