Answer
$a=5~~$ and $~~b=2$
Work Step by Step
We can multiply the first equation by 2:
$6x-4y=38$
We can multiply the second equation by -3:
$-6x+15y=-27$
We can add the two equations:
$-4y+15y = 11$
$11y = 11$
$y = 1$
We can use the first equation to find the x-coordinate:
$3x-2y = 19$
$3x-2(1) = 19$
$3x-2 = 19$
$3x = 21$
$x=7$
The point of intersection is $(7,1)$
The point of intersection is $(a+b,a-2b)$
Then:
$a+b = 7$
$a-2b = 1$
We can subtract the second equation from the first equation:
$3b = 6$
$b = 2$
Since $a+b=7$, then $a=5$
$a=5~~$ and $~~b=2$
