Question

How to solve this question simultaneously p+q=3 and 2p-q=24​

Answer 1

p=9 and q=-6

Explanation:

In algebra, we can solve systems through substitution or elimination

Solving by substituion:

p+q=3 and 2p-q=24​

In order to solve by substition, we need to isolate the variable.

p+q=3

p = -q+3

Now that we know p= -q+3, we can put it back into the other equation to solve for q.

2(-q+3)-q=24

-2q+6-q=24

-3q+6=24

-3q=18

q=-6

Now that we know q=-6, we can place it into p+q=3 to solve for p.

p-6=3

p=9

Therefore, our final answer is p=9 and q=-6

Answer 2

p = 9

q = -6

Explanation:

We can use substitution method to solve the simultaneous linear equations.

p + q = 3 -------------(I)

2p - q = 24 -------------(II)

Equation (I) can be written as, p = 3 - q -----------------(III)

Substitute p = 3 - q in equation (II),

2*(3 - q) - q = 24

Open the parenthesis by multiplying each term of (3 - q) by 2,

2*3 - 2*q - q = 24

6 - 2q - q = 24

Combine like terms,

6 - 3q = 24

Subtract 6 from both sides,

-3q = 24 - 6

-3q = 18

Divide both sides by (-3),

q = 18 ÷ (-3)

`\boxed{\bf q = -6}`

Substitute q = (-6) in equation (III),

p = 3 - (-6)

= 3 + 6

`\boxed{\bf p = 9}`