Question 849344
the 2 equations are:


y - 2 = 3x


and:


(x-2)^2 + y - 30 = 0


solve for y in terms of x in the first equation.


you will get:


y = 3x + 2


substitute for y in the second equation to get:


(x-2)^2 + (3x + 2) - 30 = 0


simplify the equation to get:


(x-2)^2 + 3x - 28 = 0


now you want to expand the equation to get:


x^2 - 4x + 4 + 3x - 28 = 0


simplify this equation to get:


x^2 - x - 24 = 0


factor this equation by use of the quadratic formula to get:


x = (1 + square root of (97)) / 2


or:


x = (1 - square root of (97)) / 2


i confirmed the first solution is correct.


if x = (1 + square root of (97)) / 2, then:


y = 3 * (1 + square root of (97)) / 2 + 2


in decimal form, these answers become:


x = 5.42443 rounded to 5 decimal places.
y = 18.27329 rounded to 5 decimal places.


replacing x and y in the original equations confirms that these solutions are good.


you can do the same with x = (1 - square root of (97)) / 2