Question 1009252

Simultaneous equations - one linear, one quadratic 
Solve the following equations:

xy = 12
x + y = 7 
<pre>xy = 12 ---------- eq (i)
x + y = 7_____x = 7 - y -------- eq (ii)
y(7 - y) = 12 ---- Substituting 7 - y for x in eq (i)
{{{7y - y^2 = 12}}}
{{{y^2 - 7y + 12 = 0}}}
(y - 4)(y - 3) = 0 
{{{highlight_green(system(y = 4_OR, y = 3))}}}
Now substitute each y value into any of the 2 original equations to determine the 2 corresponding values of x. 
You'll see that the following solutions are derived: {{{highlight_green(system(matrix(2,3, x = 3, when, y = 4_OR,x = 4,when,y = 3)))}}}