The solution to the system of equations?

Question

x + 3y= 12
4x - y = -17 is

a. (3, 3)
b. (12, -17)
c. (-3, 5)
d. (5, 3)

Answer 1

Subisitution Method

x + 3y = 12- - - - - -Equation 1
4x - y = - 15- - - - - Equation 2
- - - - - - - - --

Isolate x in equation 1

x + 3y = 12

Transpose 3y

x + 3y - 3y = - 3y + 12

collect like terms

x = - 3y + 12

Substitute the x value into equation 2
- - - - - - - - -

4x - y = - 17

4(- 3y + 12) - y = - 17

The distributive property

- 12y + 48 - y = - 17

Collect like terms

- 13y + 48 = - 17

Transpose 48

- 13y + 48 - 48 = - 17 - 48

Collect like terms

- 13y = - 65

Divide both sides of the equation by - 13

- 13y / - 13 = - 65 / - 13

y = - 65 / - 13

y = 5

Insert the y value into equation 1

- - - - - - - - -

x + 3y = 12

x + 3(5) = 12

x + 15 = 12

Transpose 15

x + 15 - 15 = 12 - 15

Collect like terms

x = - 3

Insert the x value into equation 1
- - - - - - - - -

Check for equation 1

x + 3y = 12

- 3 + 3(5) = 12

- 3 + 15 = 12

12 = 12

- - - - - - - - -

Check for equation 2

4x - y = - 17

4(- 3) - (5) = - 17

- 12 - 5 = - 17

- 17 = - 17

- - - - - - - - - -

Both equations balance

The solution set is { - 3, 5 }

The answer is c

- - - - - - - - - -s-

Answer 2

x + 3y = 12 means x = 12 - 3y
So 4(12 - 3y) - y = -17
or 48 - 12y - y = -17
or 48 - 13y = -17
or -13y = -65
or y = 5

Dead give-away. Must be C