Question

$2a(2p-q)=1$,
$p=2q-1$
Consider the system of equations above, where $a$ is a constant. For which value of $a$ is $(p,q)=(1,1)$ a solution?

• A. $2$
• B. $\frac{1}{2}$
• C. $-\frac{1}{2}$
• D. None of the above

Answer 1

The correct option is B $\frac{1}{2}$

[Beware of option D we need to check whether given values satisfy the system ]
We should first substitute (1, 1) in to the second equation to see it (1, 1) is a possible solution
$p=2q-1$
$1=2\left(1\right)-1$
1 = 1
Because the second equation created a true statement, we proceed by substituting (1, 1) into the first equation.
$2a\left(2\right(1)-1)=1$
$2a(2-1)=1$
$2a=1$
$a=\frac{1}{2}$