If the system of equations
\(\begin{align*} 3x+y&=a,\\ 2x+5y&=2a, \end{align*}\)
has a solution when \($(x,y)$\), compute \(a\)
Multiply first equation by -5 to get
-15x -5y = -5a add to second equation to get
-13x = -3a
x = 3/13 a
Now multiply second equation by - 3/2 to get
- 3x - 15/2 y = - 3a add to first equation to get
-13/2 y = -2a
y = 4/13 a sub red equations into equation one
9/13a + 4/13 a = a check ! so pick any value for a say 13 then x = 3 y = 4
or if a = 26 then x = 6 y = 8 etc sooo there is a LOT of answers unless you restrict them somehow !