Question

$8p-4t=12$
$24p+18t=36+6t$
Which of the following accurately describes all solutions to the system of equations shown above?

• A. $p=\frac{3}{2}\&t=0$
• B. $p=3\&t=3$
• C. $Thereareinfinitesolutionstothesystem.$
• D. $Therearenosolutiontothesystem.$

Answer 1

The correct option is A $p=\frac{3}{2}\&t=0$

$8p-4t=12$........(i)
$24p+12t=36$......(ii)
Lets divide equation (ii) by 3 which gives
$8p-4t=12$
Now using elimination method we add equations (ii) and (iii)
Now lets try to solve equation
$8p-4t=128p+4t=12\underset{–}{}16p=24p=\frac{24}{16}p=\frac{3}{2}$
Now put $p=\frac{3}{2}$ in previous equation to find value of t
$8p-4t=128\times \frac{3}{2}-4t=1212-4t=12-4t=0t=0$
The correct values for $p\&t$, which solves this system are $p=\frac{3}{2}\&t=0$