Question

y=x+6
2x+3y=30 find the intersection

Answer 1

Find our given information

y = x + 6       -- equation 1

2x + 3y = 30 -- equation 2

plug equation 1 into equation 2

$2x + 3(x+6) = 30\\2x + 3x + 18 = 30\\5x +18 =30\\x = 12/5 -- equation 3$

plug equation 3 into equation 1

$y = (12/5) + 6 = 42/5$

The intersection is (12/5, 42/5)

Hope that helps!