Q/2 - p/3 = 1/6
p/2 - q/6 = 5

p = 13, q = 9

Step-by-step explanation:

Given the 2 equations

- = ( multiply through by 6 to clear the fractions )

3q - 2p = 1 → (1)

- = 5 ( multiply through by 6 to clear the fractions )

3p - q = 30 , that is

- q + 3p = 30 → (2)

Multiplying (2) by 3 and adding to (1) eliminates the term in q

- 3q + 9p = 90 → (3)

Add (1) and (3) term by term to eliminate q

7p = 91 ( divide both sides by 7 )

p = 13

Substitute p = 13 into (2) for corresponding value of q

- q + 3(13) = 30

- q + 39 = 30 ( subtract 39 from both sides )

- q = - 9 ( multiply both sides by - 1 )

q = 9

Thus p = 13 and q = 9

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.